This thesis considers the design of distributed state and output feedback control algorithms for linear multi-agent systems with performance guarantees in the presence of delays. The multi-agent systems considered are assumed to exchange relative information over an information network. As a first contribution, a novel distributed state feedback control design method with a sub-optimal LQR performance is developed for a network of multiple agents. For the control design process, it is assumed that the exchange of relative information is instantaneous. A stability analysis of the proposed control law is performed by incorporating delays in relative information to ascertain the maximum possible delay that can be accommodated by the communication network. Subsequently, the assumption of the exchange of instantaneous relative information in the control design process is relaxed and the relative information is assumed to be delayed. The system is then represented as a time-delay system. Distributed state feedback control synthesis methods are then developed for the system with a certain level of LQR performance. In the above contributions, the time delay analysis and the development of delay based control methods, it is implicitly assumed that delays are detrimental to achieving cooperative tasks for a multi-agent system. Subsequently, positive effects of delays in communication of relative information are explored. For this a network of vehicles described by double integrator dynamics, which cannot be stabilized by static output feedback without delays, is considered. A novel control design method to achieve exponential stabilization of such a multi-agent system by static output feedback using delayed relative information is developed. Conclusions are drawn from the results of the research presented in this thesis and a few directions for future work are identified.

Esta tese versa sobre a síntese de compensadores antiwindup para sistemas lineares contínuos invariantes no tempo, com restrições no atuador e atraso no tempo. Baseados em um funcional Liapunov-Krasovskii e uma condição de setor para a função zona-morta já existentes na literatura, são propostas condições suficientes expressas em LMIs para a existência de compensadores antiwindup para duas classes de sistemas: sistemas com atraso nos estados, e sistemas com atraso na entrada. Em ambos os casos, considera-se a síntese de um compensador de ordem plena para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores antiwindup considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, e um conjunto de inicialização dos estados do sistema tolerante à perturbação com norma L2 inferior a um máximo, determinado juntamente com a síntese do compensador antiwindup. Na ausência de perturbação a origem é garantida assintoticamente estável. Para sistemas com atraso no estado, primeiro propõe-se um método para a síntese de compensadores dinâmicos racionais de ordem plena. Este método é baseado no Lema de Projeção. Em seguida, estende-se o resultado, propondo-se um framework genérico que permite a síntese de compensadores racionais e não racionais. Este método é baseado em uma transformação de variáveis linearizante. Para sistemas com atraso na entrada, propõe-se três resultados de síntese de compensadores antiwindup: compensadores estáticos, dinâmicos racionais, e dinâmicos não racionais. Estes métodos são novamente baseados no Lema de Projeção. Em todos os casos, as condições obtidas que garantem a existência de um compensador antiwindup são expressas em forma de LMIs e garantem a estabilidade local da origem. Em seguida, estende-se os resultados para garantir a estabilidade global da origem, nos casos em que a planta é estável em malha aberta. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída regulada. Exemplos numéricos ilustram cada método na solução dos problemas de máxima tolerância à perturbação, e minimização do ganho L2 da perturbação à saída regulada. / This thesis verses about antiwindup compensator synthesis for linear time invariant continuous systems, presenting constraints in actuator and time delay. Based on a Liapunov-Krasovskii functional and a sector condition for the dead-zone nonlinearity already castign in literature, it is proposed sufficient conditions expressed in LMI to the existance of an antiwindup compensator for two classes of systems: systems with state delay, and systems with input delay. In both cases it is considered the synthesis of a full order antiwindup compensator for a system with a controller a priori given that disregards the actuator bounds. The synthesis of antiwindup compensators considers an actuator constrained in amplitude and a system subjected to norm-L2 bounded disturbances. Once the casted conditions are verified, it is assured the closed loop origin stability; a set for the initial states of the system tolerating disturbances up to a maximum L2 norm, which is also determined along the antiwindup compensator synthesis procedure. In the absence of disturbance the origin is assuredly asymptotically stable. For state delay systems, first it is proposed a method for designing full order rational antiwindup compensators. This method is based on the Projection Lemma. Afterwards, results are extended proposing a generic framework allowing the synthesis of rational and nonrational compensators of different topologies. This method is based on a linearizing variable transformation. For input delay systems, it is proposed three synthesis results: static, rational dynamic and nonrational dynamic compensators. These methods are based on the Projection Lemma. In all cases, the conditions obtained assuring the existance of an antiwindup compensator are expressed by means of LMIs that, once verified, assure the origin local stability. Then, the conditions are extended for the global stability case, when the system is open loop stable. Optimization problems are proposed for both methods to maximize the disturbance tolerance and the minimization of the L2-gain of the disturbance to the regulated output. Numerical examples are presented to illustrate each method in the solution of the problems of maximum disturbance tolerance, and minimization of L2-gain from the disturbance to the regulated output.

Esta tese versa sobre a síntese de compensadores antiwindup para sistemas lineares contínuos invariantes no tempo, com restrições no atuador e atraso no tempo. Baseados em um funcional Liapunov-Krasovskii e uma condição de setor para a função zona-morta já existentes na literatura, são propostas condições suficientes expressas em LMIs para a existência de compensadores antiwindup para duas classes de sistemas: sistemas com atraso nos estados, e sistemas com atraso na entrada. Em ambos os casos, considera-se a síntese de um compensador de ordem plena para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores antiwindup considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, e um conjunto de inicialização dos estados do sistema tolerante à perturbação com norma L2 inferior a um máximo, determinado juntamente com a síntese do compensador antiwindup. Na ausência de perturbação a origem é garantida assintoticamente estável. Para sistemas com atraso no estado, primeiro propõe-se um método para a síntese de compensadores dinâmicos racionais de ordem plena. Este método é baseado no Lema de Projeção. Em seguida, estende-se o resultado, propondo-se um framework genérico que permite a síntese de compensadores racionais e não racionais. Este método é baseado em uma transformação de variáveis linearizante. Para sistemas com atraso na entrada, propõe-se três resultados de síntese de compensadores antiwindup: compensadores estáticos, dinâmicos racionais, e dinâmicos não racionais. Estes métodos são novamente baseados no Lema de Projeção. Em todos os casos, as condições obtidas que garantem a existência de um compensador antiwindup são expressas em forma de LMIs e garantem a estabilidade local da origem. Em seguida, estende-se os resultados para garantir a estabilidade global da origem, nos casos em que a planta é estável em malha aberta. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída regulada. Exemplos numéricos ilustram cada método na solução dos problemas de máxima tolerância à perturbação, e minimização do ganho L2 da perturbação à saída regulada. / This thesis verses about antiwindup compensator synthesis for linear time invariant continuous systems, presenting constraints in actuator and time delay. Based on a Liapunov-Krasovskii functional and a sector condition for the dead-zone nonlinearity already castign in literature, it is proposed sufficient conditions expressed in LMI to the existance of an antiwindup compensator for two classes of systems: systems with state delay, and systems with input delay. In both cases it is considered the synthesis of a full order antiwindup compensator for a system with a controller a priori given that disregards the actuator bounds. The synthesis of antiwindup compensators considers an actuator constrained in amplitude and a system subjected to norm-L2 bounded disturbances. Once the casted conditions are verified, it is assured the closed loop origin stability; a set for the initial states of the system tolerating disturbances up to a maximum L2 norm, which is also determined along the antiwindup compensator synthesis procedure. In the absence of disturbance the origin is assuredly asymptotically stable. For state delay systems, first it is proposed a method for designing full order rational antiwindup compensators. This method is based on the Projection Lemma. Afterwards, results are extended proposing a generic framework allowing the synthesis of rational and nonrational compensators of different topologies. This method is based on a linearizing variable transformation. For input delay systems, it is proposed three synthesis results: static, rational dynamic and nonrational dynamic compensators. These methods are based on the Projection Lemma. In all cases, the conditions obtained assuring the existance of an antiwindup compensator are expressed by means of LMIs that, once verified, assure the origin local stability. Then, the conditions are extended for the global stability case, when the system is open loop stable. Optimization problems are proposed for both methods to maximize the disturbance tolerance and the minimization of the L2-gain of the disturbance to the regulated output. Numerical examples are presented to illustrate each method in the solution of the problems of maximum disturbance tolerance, and minimization of L2-gain from the disturbance to the regulated output.

Esta tese versa sobre a síntese de compensadores antiwindup para sistemas lineares contínuos invariantes no tempo, com restrições no atuador e atraso no tempo. Baseados em um funcional Liapunov-Krasovskii e uma condição de setor para a função zona-morta já existentes na literatura, são propostas condições suficientes expressas em LMIs para a existência de compensadores antiwindup para duas classes de sistemas: sistemas com atraso nos estados, e sistemas com atraso na entrada. Em ambos os casos, considera-se a síntese de um compensador de ordem plena para um sistema com um controlador dado a priori desprezando limites do atuador. A síntese dos compensadores antiwindup considera um atuador restrito em amplitude e o sistema sujeito a perturbações limitadas em norma L2. A verificação das condições enunciadas garante a estabilidade da origem em malha fechada, e um conjunto de inicialização dos estados do sistema tolerante à perturbação com norma L2 inferior a um máximo, determinado juntamente com a síntese do compensador antiwindup. Na ausência de perturbação a origem é garantida assintoticamente estável. Para sistemas com atraso no estado, primeiro propõe-se um método para a síntese de compensadores dinâmicos racionais de ordem plena. Este método é baseado no Lema de Projeção. Em seguida, estende-se o resultado, propondo-se um framework genérico que permite a síntese de compensadores racionais e não racionais. Este método é baseado em uma transformação de variáveis linearizante. Para sistemas com atraso na entrada, propõe-se três resultados de síntese de compensadores antiwindup: compensadores estáticos, dinâmicos racionais, e dinâmicos não racionais. Estes métodos são novamente baseados no Lema de Projeção. Em todos os casos, as condições obtidas que garantem a existência de um compensador antiwindup são expressas em forma de LMIs e garantem a estabilidade local da origem. Em seguida, estende-se os resultados para garantir a estabilidade global da origem, nos casos em que a planta é estável em malha aberta. Problemas de otimização são propostos para ambos os métodos para maximizar a tolerância à perturbação e a minimização do ganho L2 da perturbação à saída regulada. Exemplos numéricos ilustram cada método na solução dos problemas de máxima tolerância à perturbação, e minimização do ganho L2 da perturbação à saída regulada. / This thesis verses about antiwindup compensator synthesis for linear time invariant continuous systems, presenting constraints in actuator and time delay. Based on a Liapunov-Krasovskii functional and a sector condition for the dead-zone nonlinearity already castign in literature, it is proposed sufficient conditions expressed in LMI to the existance of an antiwindup compensator for two classes of systems: systems with state delay, and systems with input delay. In both cases it is considered the synthesis of a full order antiwindup compensator for a system with a controller a priori given that disregards the actuator bounds. The synthesis of antiwindup compensators considers an actuator constrained in amplitude and a system subjected to norm-L2 bounded disturbances. Once the casted conditions are verified, it is assured the closed loop origin stability; a set for the initial states of the system tolerating disturbances up to a maximum L2 norm, which is also determined along the antiwindup compensator synthesis procedure. In the absence of disturbance the origin is assuredly asymptotically stable. For state delay systems, first it is proposed a method for designing full order rational antiwindup compensators. This method is based on the Projection Lemma. Afterwards, results are extended proposing a generic framework allowing the synthesis of rational and nonrational compensators of different topologies. This method is based on a linearizing variable transformation. For input delay systems, it is proposed three synthesis results: static, rational dynamic and nonrational dynamic compensators. These methods are based on the Projection Lemma. In all cases, the conditions obtained assuring the existance of an antiwindup compensator are expressed by means of LMIs that, once verified, assure the origin local stability. Then, the conditions are extended for the global stability case, when the system is open loop stable. Optimization problems are proposed for both methods to maximize the disturbance tolerance and the minimization of the L2-gain of the disturbance to the regulated output. Numerical examples are presented to illustrate each method in the solution of the problems of maximum disturbance tolerance, and minimization of L2-gain from the disturbance to the regulated output.

Το ερευνητικό αντικείμενο της Διατριβής είναι τα θέματα σθεναρότητας του προκύπτουν στα Δικτυωμένα Συστήματα Ελέγχου (Νetworked Cοntrοlled Systems - εφεξής "ΝCS"), όπου η βασική πηγή αβεβαιότητας είναι οι καθυστερήσεις λόγω δικτύου. Στο πλαίσιο αυτό παρουσιάζονται απότελέσματα του αφορούν στην ανάλυση σθεναρής ευστάθειας και στην σύνθεση σθεναρών ελεγκτών. Να επισημανθεί ότι στην Διατριβή, ο προσδιορισμός "σθεναρός" αφορά απόκλειστικά σθεναρότητα (ευστάθειας και επιδόσεων) ως προς τις αβέβαιες, χρονικά μεταβαλλόμενες, φραγμένες καθυστερήσεις. Τα μελετώμενα ΝCS απαρτίζονται από την διασύνδεση γραμμικών χρονικά αμετάβλητων συστημάτων συνεχούς χρόνου με ελεγκτές διακριτού χρόνου. Η βασική διάρθρωση των συστημάτων αυτών απαρτίζεται από έναν "οδηγούμενο από χρόνο" (time driven) αισθητήρα / δειγματολήπτη (με σταθερή περίοδο δειγματοληψίας h) που μεταδίδει μέσω του δικτύου τα δείγματα που λαμβάνει από το σύστημα στον "οδηγούμενο από γεγονότα" (event–driven) ελεγκτή. Ακολούθως ο ελεγκτής υπολογίζει την δράση ελέγχου και την μεταδίδει μέσω του δικτύου στον "οδηγούμενο από γεγονότα" (eveτιt–driven) ενεργοποιητή. Οι διαδικασίες της μοντελοποίησης, της ανάλυσης ευστάθειας και της σύνθεσης σθεναρών ελεγκτών (στατικών αλλά και κατά τμήματα γραμμικών) στην εργασία αυτή λαμβάνουν χώρα στο πεδίο του διακριτού χρόνου μετά από διακριτοποίηση του συνολικού συστήματος. Όσον αφορά στην ανάλυση σθεναρής ευστάθειας προτείνονται δύο προσεγγίσεις: • η πρώτη, βασιζόμενη σε ανάλυση ιδιαζουσών τιμών, είναι υπολογιστικά ελκυστική αλλά συνήθως δίδει συντηρητικά αποτελέσματα, • ενώ η δεύτερη, διατυπωμένη σαν ανισότητα πινάκων (LMI), είναι απαιτητική ως προς τον χρόνο υπολογισμού αλλά δίδει αποτελέσματα με μειωμένο συντηρητισμό. Όσον αφορά στην σύνθεση σθεναρών ελεγκτών ανατροφοδότησης κατάστασης μελετώνται οι εξής προσεγγίσεις: • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης "εγγυημένου κόστους" που απαντάει στην συνδυασμένη απαίτηση ευστάθειας και επίδοσης • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Cοnstrained Controller) για ΝCS με "μικρή καθυστέρηση". Επέκταση των αποτελεσμάτων για ΝCS με "μεγάλη καθυστέρηση". Εφαρμογή των παραπάνω αποτελεσμάτων σε προβλήματα παρακολούθησης σταθερής εντολής (set point tracking). • Σύνθεση σθεναρής ευσταθειοποιούσας ανατροφοδότησης κατάστασης με περιορισμό (Constrained Controller), για ΝCS με μικρή και διακοπτική καθυστέρηση. / This research work is concerned with robustness issues arising in Νetworked Cοntrοlled Systems - ("ΝCS"), where the main sources of uncertainty are the time-varying network-induced delays. In this framework the presented results concern robust stability analysis and synthesis of robust controllers. The NCS studied consist of a Linear Time Invariant continuous time plant and a discrete time controller. This configuration includes a time driven (periodic) sampler (taking samples from the sensors with constant sampling period h) and an event–driven controller which transmits the control command via the network to the event–driven actuator. Two modeling approaches for Networked Controlled Systems (NCS) with uncertainly varying bounded transmission delays and static discrete--time control laws are presented. Different models are offered for each case, all linked to the objective of designing robust discrete-time controllers. It is analytically shown how the careful mixing of asynchronous (event--driven) and synchronized (clocked) signals can lead to discrete time uncertain (possibly switched) systems, where results form robust control analysis and synthesis can be applied. After showing the implications of these modelling results for control synthesis purposes, sufficient conditions for the robust stability are given for each approach and a comparison of the conservatism of results is discussed The first group of robust stability results (one for each of the two discrete-time NCS models) is based on a singular value formulation, which although conservative, is extremely simple and has low computational cost The second one is derived and expressed via Linear Matrix Inequalities (LMI) and yields less conservative results at the expense of higher computational cost. Regarding the synthesis of Robust controllers, the following four methodologies were developed: 1. Synthesis of Robust Static State feedback 2. Synthesis of Robust Static State feedback via the “Guaranteed Cost Formulation” which combines stability and performance design objectives 3. Synthesis of Constrained Robust feedback controller (with a Piecewise Affine Structure) which respects the constraints on the control effort and the state (or output). 4. The previous result (Constrained Robust feedback controller) is then generalized for set-point tracking and for various types of network-induced delays (small, large and switching delays)

Cette thèse concerne la stabilisation exponentielle de systèmes commandés en réseaux (NCS en anglais) par retour de sortie. Les solutions proposées reposent sur un observateur distant et capable d’estimer l’état présent du processus malgré les différents retards générés par la présence du réseau. Le premier chapitre présente le contexte général des NCS et décrit plus particulièrement le problème étudié. Le chapitre suivant propose une architecture informatique permettant de réaliser un retour d’état distant basé sur une structure d’observateur. Deux autres chapitres proposent ensuite la synthèse d’un couple loi de commande / observateur garantissant des performances de convergence exponentielle. Les conditions correspondantes s’écrivent sous forme d’inégalités matricielles linéaires (LMI en anglais) et permettent donc une optimisation. Ces conditions sont basées sur la méthode des fonctionnelles de Lyapunov-Krasovskii et des résultats originaux sont proposés. Une première synthèse peut être effectuée globalement, une seconde permet d’adapter les performances dynamiques à la qualité de service disponible à chaque instant. La seconde approche fait intervenir des résultats originaux sur les systèmes à retards et à commutations. Dans un dernier chapitre, nous proposons une solution complètement asynchrone (gérée par événements). Dans ce cas, le problème des pertes de paquets devient crucial et nous y apportant une réponse. L’ensemble des résultats est confirmé par des expérimentations mises au point dans le cadre de ce travail, et correspondant à un robot léger commandé en temps réel à 40km de distance par Internet / This PhD thesis is dedicated to the exponential output stabilization of linear NCS (Networked Control Systems). The studied solution is based on a remote observer which is able to estimate the present state of the plant despite the various network induced delays. These last are present in both the control and the measurement channels.The first chapter describes the problem and gives a survey on the NCS. The next chapter proposes a computer structure which realizes the remote, observer-based, state feedback controller. The following two chapters propose LMI conditions (Linear Matrix Inequalities) for the design of the observer-based remote controller. The second method of Lyapunov is used with the most up-to-date Lyapunov-Krasovskii functionals. The main objective of the design is to guarantee some performances expressed in the form of exponential stability. Then some enhancements of the control strategy are given. It consists in taking into account the Quality of Service (QoS) in the controller to get better guaranteed performances. The last contribution of this work is to consider the overall system as an event-driven system. It allows one to consider packet dropout problems in the network.The effectiveness of all presented results is demonstrated by real experiments implemented on a light robot controlled over the Internet

Made available in DSpace on 2014-06-11T19:30:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-12Bitstream added on 2014-06-13T20:40:35Z : No. of bitstreams: 1 mendes_rat_dr_ilha.pdf: 2326436 bytes, checksum: 60aa15eb5fb66a63b31662bee7904bfa (MD5) / Neste trabalho sao propostas metodologias de modificacao de zeros para solucionar o problema do rastreamento do sinal de referencia em sistemas discretos determinısticos, sistemas discretos incertos e sistemas discretos nao-lineares considerando-se uma entrada de perturbacao na planta. Em um primeiro momento e projetado um controlador discreto para minimizar a norma H∞ entre a entrada ex´ogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema determinıstico. Posteriormente, minimiza-se a norma H∞ entre o sinal de referencia e o erro de rastreamento atraves da modificacao otima de zeros do sistema discreto, constituindo desta maneira o rastreador de sinal de referencia. Essa nova estrutura de projeto do controlador e estendida para o projeto do controlador robusto H∞, supondo incertezas politopicas na planta e tambem para sistemas nao-lineares. No caso de sistemas com incertezas politopicas na planta, um controlador discreto e projetado para minimizar o custo garantido H∞ entre a entrada exogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema discreto incerto. Posteriormente e projetado um rastreador para sinais de referˆencia em sistemas com incertezas politopicas, utilizando-se modificacao de zeros. Por fim, estende-se a metodologia de rastreamento do sinal de referencia com rejeicao do disturbio para sistemas nao-lineares. A formulacao do projeto e descrita na forma de inequacoes matriciais lineares, pois estas permitem a descricao de problemas de otimizacao convexa / The tracking problems in uncertain, deterministic and nonlinear discrete time systems, with the presence of a disturbance signal in the plant, are solved in this work proposing a zero variation methodology. A discrete state feedback controller is designed in order to minimize the H∞-norm between the exogen input and the output signal, such that the effect of the disturbance is attenuated in deterministic systems. After, the tracking problem is solved using the variation of the zeros minimizing the H∞-norm from the reference input signal to the error tracking signal. This new structure is extended to design of H∞ robust controller, supposing politopic uncertainties and other one supposing nonlinearities in the plant. In uncertain systems case, a discrete controller is designed in order to minimize the H∞ guaranteed cost between the exogen input and the output signal such that the effect of the disturbance is attenuated in uncertain systems. Then, the tracking problem in uncertain systems is solved using the variation of the zeros minimizing the H∞ guaranteed cost from the reference input signal to the error tracking signal. Finally, the zero variation methodology is extended to nonlinear systems. The design is formulated in the Linear Matrix Inequalities (LMI) framework, such that the optimal solution of the stated control problem is obtained when feasible solution exists

Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: José Paulo Fernandes Garcia / Banca: Cristiano Quevedo Andrea / Banca: Márcio Roberto Covacic / Resumo: Neste trabalho sao propostas metodologias de modificacao de zeros para solucionar o problema do rastreamento do sinal de referencia em sistemas discretos determinısticos, sistemas discretos incertos e sistemas discretos nao-lineares considerando-se uma entrada de perturbacao na planta. Em um primeiro momento e projetado um controlador discreto para minimizar a norma H∞ entre a entrada ex'ogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema determinıstico. Posteriormente, minimiza-se a norma H∞ entre o sinal de referencia e o erro de rastreamento atraves da modificacao otima de zeros do sistema discreto, constituindo desta maneira o rastreador de sinal de referencia. Essa nova estrutura de projeto do controlador e estendida para o projeto do controlador robusto H∞, supondo incertezas politopicas na planta e tambem para sistemas nao-lineares. No caso de sistemas com incertezas politopicas na planta, um controlador discreto e projetado para minimizar o custo garantido H∞ entre a entrada exogena e o sinal de saıda com o objetivo de reduzir o efeito da perturbacao sobre a saıda do sistema discreto incerto. Posteriormente e projetado um rastreador para sinais de referˆencia em sistemas com incertezas politopicas, utilizando-se modificacao de zeros. Por fim, estende-se a metodologia de rastreamento do sinal de referencia com rejeicao do disturbio para sistemas nao-lineares. A formulacao do projeto e descrita na forma de inequacoes matriciais lineares, pois estas permitem a descricao de problemas de otimizacao convexa / Abstract: The tracking problems in uncertain, deterministic and nonlinear discrete time systems, with the presence of a disturbance signal in the plant, are solved in this work proposing a zero variation methodology. A discrete state feedback controller is designed in order to minimize the H∞-norm between the exogen input and the output signal, such that the effect of the disturbance is attenuated in deterministic systems. After, the tracking problem is solved using the variation of the zeros minimizing the H∞-norm from the reference input signal to the error tracking signal. This new structure is extended to design of H∞ robust controller, supposing politopic uncertainties and other one supposing nonlinearities in the plant. In uncertain systems case, a discrete controller is designed in order to minimize the H∞ guaranteed cost between the exogen input and the output signal such that the effect of the disturbance is attenuated in uncertain systems. Then, the tracking problem in uncertain systems is solved using the variation of the zeros minimizing the H∞ guaranteed cost from the reference input signal to the error tracking signal. Finally, the zero variation methodology is extended to nonlinear systems. The design is formulated in the Linear Matrix Inequalities (LMI) framework, such that the optimal solution of the stated control problem is obtained when feasible solution exists / Doutor