En aquesta tesi, presentem una solució per a dos problemes rellevants en la teoria de control: el problema del cost quadràtic garantit i el problema del control H∞, per a un cert tipus de sistemes. Considerem els sistemes interconnectats lineals amb incerteses, sota la presència de fallades en els actuadors, i dissenyem controls descentralitzats que a més a més d'assegurar estabilitat, resolen aquests dos problemes. Treballem amb tres models diferents d'incerteses: incerteses normades o acotades, incerteses definides sobre un politop i incerteses que segueixen el model multiconvex. El model de fiabilitat emprat permet plantejar-se tant una fallada total en l'actuador com una fallada parcial. Els dos problemes tractats són:· Problema del control RGC. Sintetitzar el control fiable sota fallada en els actuadors, que assegura estabilitat i garanteix un cert nivell de rendiment o de cost, calculant una cota mínima per a la funció de cost.· Problema del control robust. Dissenyar el control que assegura estabilitat interna sota pertorbacions en el sistema, obtenint una cota per a la relació entre la pertorbació i la sortida controlable. Es considera la norma H∞ del sistema, que representa l'increment màxim en energia, entre l'entrada i la sortida del sistema..A l'hora de dissenyar ambdos controls, utilitzem les tècniques donades per les inequacions lineals matricials (LMI), que permeten una fàcil implementació numèrica. Així doncs, a part de tractar els problemes de la llei RGC i del control robust, hem determinat una relació general entre inequacions matricials lineals i no lineals, que permet obtenir caracteritzacions LMI per a un gran ventall de problemes de teoria de control. Les LMI que hem obtingut separen les dades del problema i les variables de disseny, permetent una resolució menys restrictiva. En particular, faciliten l'ús de funcions de Lyapunov paramètriques que asseguren l'estabilitat del sistema quan una funció no paramètrica no arriba a fer-ho. La formulació per mitjà de les tècniques LMI ens ha permès obtenir implementacions numèriques efectives, així com relaxacions en les condicions d'estabilitat. En el cas del problema del control RGC, trobem que quan es consideren fallades en el sistema, el model d'incerteses es veu reduït en certa manera, perdent també llibertat en la definició de la funció de cost. Un cop sintetitzat el control RGC, presentem dues maneres que permeten obtenir una cota òptima del cost garantit, així com treure'n la dependència respecte les condicions inicials. Hem dut a terme exemples numèrics que mostren l'eficiència dels mètodes enunciats, tractant els models d'incerteses normat i politòpic. Els resultats s'han obtingut usant el Toolbox LMI Control del programa Matlab.El segon problema que ens plantejem és el del control estàtic realimentat per l'estat, tal que la norma H∞ del sistema es troba acotada. Aquest fet assegura que l'efecte de pertorbacions en el sistema està dins de marges desitjats. A més a més, la síntesi obtinguda és independent del model de incerteses i, en el cas dels models normat i politòpic, hem obtingut una caracterització LMI. També fem un breu estudi del control robust realimentat per la sortida, obtenint una caracterització en termes LMI, en el cas que no se suposin errors en la medició de la sortida. / This thesis presents a design of a reliable decentralized state feedback control for a class of uncertain interconnected systems. We present a solution for two outstanding problems in the control theory: the problem of the guaranteed quadratic cost control and the H∞ problem. We have designed decentralized controls that besides assuring stability, they solve these two problems. We have considered three uncertainty models: born-normed model, polytopic model and multiconvex model. A model of failures in actuators is adopted which considers outages or partial degradation in independent actuators. The two treated problems are: · RGC Control. This problem is related to the decentralized reliable guaranteed cost control problem for interconnected systems. The presented reliable control shows that the admission of control failures imposes some restriction in the control weighting matrices in the performance criterion. Thus the designer can take some trade-off between control performance and admitted reliability.· Robust Control. The control problem considered is to design feedback controller, such that the closed loop structure is stable and has a specified performance. In the standard H problem, stability means internal stability and the performance is taken to be the H norm of the transfer function from the exogenous inputs and the regulators outputs. An estimation of worst-case H norm is required. A key point in the control design has been the formulation of a new linear matrix inequality (LMI) characterization, which uses parameter-dependent Lyapunov functions and slack variables. The obtained LMI separate the unknown variables from the system parameter data, which smoothes the numerical solution. This characterization can be useful for different classes of problems, such as guaranteed cost control, H2 or H∞ control design.We use this type of LMI to proof that the proposed decentralized control scheme guarantees the quadratic stability and a cost bound, for RGC control problem, and a H∞ norm bound for a robust control problem, for a class of failure model which considers outage or partial degradation of any independent specific actuator. We make this for the three uncertainties models. A numerical example has been included to illustrate the proposed decentralized control approach. Computations have been made by using standard Matlab's LMI Control Toolbox.

The thesis considers the problems of designing a dynamic output feedback controller to discrete time systems with polytopic uncertainty so that the closed-loop systems are DR stable with their transfer matrices having H2 norm and H¡Û norm bounded by a prescribed value ru. The formar part of the thesis provides less conservative LMI conditions for H2 and H¡Û analysis and the output feedback control of discrete system than those appeared in the current research. While the latter part of the thesis extend the current research to DR stable with H2 and H¡Û design. Finally, numerical examples are illustrated to show improvement of the propered result.

In this dissertation, the stabilization problem and observer-based control of neutral systems are investigated. Firstly, the Lyapunov functional theory is used to guarantee the stability of the system under consideration. The delay-dependent and the delay-independent stabilization criteria are proposed to guarantee asymptotic stability for the neutral systems via linear control. Linear matrix inequality (LMI) approach is used to design the observer and the controller. Secondly, by using the same techniques, we will provide an observer-based controller design method. The delay-dependent and the delay-independent stabilization criteria are proposed to guarantee asymptotic stability for the neutral systems with multiple time delays. Finally, a guaranteed-cost observer-based control for the neutral systems is considered. The analysis is also based on Lyapunov functional so as to establish an upper bound on the closed-loop value of a quadratic cost function. Delay-independent stabilization criterion is proposed to guarantee asymptotic stability for the neutral systems via linear control. By using the LMI approach, we will provide a criterion to design the observer gain and the controller gain simultaneously. Some examples and computer simulation results will also be provided to illustrate our main results.

This thesis presents strict LMI conditions for the bounded real lemma of discrete descriptor systems. Compared with existing nonstrict LMI conditions, the proposed new conditions are more tractable and reliable in numerical computations, in the sense that they can be tested easily by using the LMI Control Toolbox of Matlab. Based on the strict LMI conditions, the state feedback design for H-infinite control problem is also addressed. A sufficient LMI condition is derived so that the constructed feedback gain matrix from its solution will meet the design criteria of the closed-loop systems. Furthermore, we can probe into the problems of robust H-infinite control and pole-clustering in a disk for uncertain discrete descriptor systems subject to time-invariant norm-bounded uncertainty and convex polytopic uncertainty in the state matrix, respectively. Some sufficient LMI conditions are derived for analysis and design of these problems as well. Numerical examples are included to illustrate the results.

In this dissertation, we will investigate the global stability for some uncertain neural networks with multiple time-varying delays. These well-known neural networks include delayed cellular neural networks (DCNNs), delayed bidirectional associative memory neural networks (DBAMNNs), and delayed Cohen-Grossberg neural networks (DCGNNs). Delay-dependent and delay-independent criteria will be proposed to guarantee the robust stability of these uncertain delayed neural networks via linear matrix inequality (LMI) approach. Three types of uncertainties on feedback and delayed feedback matrices in these uncertain delayed neural networks will be considered in this study, namely uncertainties with structured perturbation, norm-bounded unstructured perturbation, and interval perturbation. Some numerical examples will be given to illustrate the effectiveness of our results. Some comparisions are made to show that our results are better than some results in recent literature.

Cette thèse se focalise sur une classe particulière de modèles non linéaires appelés<br />modèles Takagi-Sugeno. Même s'ils sont issus de l'approche historique de la logique<br />floue, ils peuvent s'interpréter comme une collection de modèles linéaires interconnectés<br />par des fonctions non linéaires.<br />L'étude de la stabilité de ces types de modèles fait appel, dans la grande majorité des cas,<br />à la méthode directe de Lyapunov avec une fonction de type quadratique. Celle-ci<br />permettant écrire facilement des conditions sous la forme de contraintes LMI. Les<br />conditions obtenues ne sont que suffisantes.<br />De nombreux résultats sont disponibles aujourd'hui pour ce type de modèles. Les<br />premiers travaux ne traitaient que de la stabilité et de stabilisation sans critères de<br />robustesse ou notions de performances. Depuis des extensions à des retours d'état avec<br />observateur, à des modèles sous forme descripteur, à des modèles incertains, à des<br />modèles à retard à des modèles incertains à retard, à des retours de sortie dynamiques,...<br />existent. Des critères de performances ont aussi été considérés comme la minimisation<br />d'un critère quadratique, D-stabilité, Hinf,...<br />En dépit de cette multitude de résultats, il reste un certain nombre de problèmes à<br />résoudre. L'approche par fonction de Lyapunov quadratique semble avoir atteint ces<br />limites. Les conditions obtenues étant seulement suffisantes le principal problème est de<br />savoir que faire si elles sont trop restrictives ? Comment relâcher un problème LMI qui<br />n'a pas de solution ? Le but de ce mémoire est de sortir du cadre des fonctions de<br />Lyapunov quadratiques en proposant des résultats moins conservatifs que ceux rencontrés<br />dans la littérature..

Networked control systems (NCSs) are feedback control systems with the feedback control loops closed via network. The origin of the term NCSs is from industrial systems where the plant and controller are often connected through networks. The applications of NCSs cover a wide range of industries, for example, manufactory automation, domestic robots, aircraft, automobiles and tele-operations. The research activities in NCSs are focused on the following three areas: control of networks, control over networks and multi-agent systems. Control of networks is mainly concerned with the problem of how to efficiently utilize the network resource by controlling and routing the network data flows. Control over networks is mainly concerned with the design of feedback control strategies of control systems in which signals are transmitted through unreliable communication links. Multi-agent systems deal with two problems: how the topology of the network connections between each component influences global control goals and how to design local control law describing the behavior of each individual to achieve the global control goal of the whole systems. The objective in this thesis is to deal with control over networks and multi-agent systems. The most challenging problem in the control over networks field is that the unreliable communication channels can degrade system performance greatly. The main unreliable properties of networks are delays and packet loss. In order to deal with this problem, a Lyapunov-based method has been used to design the sampled-data stabilization control strategy for a networked single system by choosing proper delay and packet loss dependent Lyapunov functional candidates. Linear matrix inequality techniques have been used to find the sufficient and necessary conditions for the controller design. Furthermore, the consensus formation control problem of multiple robotic vehicle systems has been investigated. The consensus-based design scheme has been applied to the formation control of multiple wheeled mobile-robot group with a virtual leader. A novel delay-dependent Lyapunov functional candidate has been constructed to investigate the convergence of the system states. The proposed control strategy is experimentally implemented for multiple wheeled mobile robots under neighbor-to-neighbor information exchange with group communication delays involved. In conclusion, through the simulation results and experimental validations, the proposed new Lyapunov-based control methods can effectively deal with the networked control systems discussed in this thesis.

Cette thèse porte sur la commande robuste des systèmes linéaires périodiques qui constituent une classe particulière de systèmes variant dans le temps. Des dynamiques périodiques apparaissent dans de nombreux domaines des sciences de l'ingénieur tels que l'aéronautique, l'espace ou les systèmes de télécommunication. Des méthodes systématiques pour l'analyse et la synthèse robuste de ces systèmes sont proposées. Le cadre de travail choisi est celui de la théorie de Lyapunov et fait appel principalement à des outils numériques de type inégalités matricielles linéaires (LMI). La robustesse est envisagée de manière duale par la prise en compte d'incertitudes pouvant non seulement affecter le système à commander mais également le correcteur lui même. Ce dernier problème est traité par la synthèse d'ensembles convexes de correcteurs assurant un certain niveau de performances garanties vis-à-vis du système bouclé. La question de la structure temporelle du correcteur est également posée. Le correcteur doit il nécessairement être de même périodicité que le système? Est-il possible de réduire le nombre de paramètres à mémoriser? Pour répondre à ces différentes questions, nous avons défini la classe des correcteurs périodiques structurés dans le temps et développé des méthodes de synthèse adaptées. Les résultats théoriques sont illustrés sur le problème du maintien à poste autonome d'un satellite en orbite basse consistant à maintenir un satellite sur une orbite de référence excentrique malgré les différentes forces perturbatrices pouvant l'en écarter (frottement atmosphérique, effet de la distribution non-sphérique de la masse de la Terre). Différentes lois de commande minimisant certains critères de performances tels que la quantité de carburant consommée ou l'influence d'accélérations perturbatrices sont calculées. Leur qualité est ensuite évaluée à l'aide de simulations non-linéaires.

Numerical methods of designing control systems are currently an active area of research. Convex optimization with linear matrix inequalities (LMIs) is one such method. Control objectives like minimizing the H_2, H_infinity norms, limiting the actuating effort to avoid saturation, pole-placement constraints etc., are cast as LMIs and an optimal feedback controller is found by making use of efficient interior-point algorithms. A full-state feedback controller is designed and implemented in this thesis using this method which then forms the basis for designing a static output feedback (SOF) controller. A profile was generated that relates the change in the SOF control gain matrix required to keep the same value of the generalized H_2 norm of the transfer function from the road disturbance to the actuating effort with the change in the sprung mass of the quarter-car system. The quarter-car system makes use of a linear brushless permanent magnet motor (LBPMM) as an actuator, a linear variable differential transformer (LVDT) and two accelerometers as sensors for feedback control and forms a platform to test these control methodologies. For the full-state feedback controller a performance measure (H_2 norm of the transfer function from road disturbance to sprung mass acceleration) of 2.166*10^3 m/s^2 was achieved ensuring that actuator saturation did not occur and that all poles had a minimum damping ratio of 0.2. The SOF controller achieved a performance measure of 1.707*10^3 m/s^2 ensuring that actuator saturation does not occur. Experimental and simulation results are provided which demonstrate the effectiveness of the SOF controller for various values of the sprung mass. A reduction in the peak-to-peak velocity by 73 percent, 72 percent, and 71 percent was achieved for a sprung mass of 2.4 kg, 2.8 kg, and 3.4 kg, respectively. For the same values of the sprung mass, a modified lead-lag compensator achieved a reduction of 79 percent, 77 percent and, 69 percent, respectively. A reduction of 76 percent and 54 percent in the peak-to-peak velocity was achieved for a sprung mass of 6.0 kg in simulation by the SOF controller and the modified lead-lag compensator, respectively. The gain of the modified lead-lag compensator needs to be recomputed in order to achieve a similar attenuation as that of the SOF controller when the value of the sprung mass is changed. For a sprung mass of 3.4 kg and a suspension spring stiffness of 1640 N/m the peak-to-peak velocity of the sprung mass was attenuated by 42 percent.

Este trabalho apresenta uma nova metodologia para a síntese simultânea de controlador e laço anti-windup visando o problema de seguimento de referências em sistemas sujeitos à saturação. Além do projeto dos controladores, será apresentada uma estimativa dos domínios de estabilidade e do conjunto de referências admissíveis. O seguimento de referências constantes e a rejeição de perturbações, também constantes, será garantido pelo princípio do modelo interno, ou seja, uma ação integral será adicionada a uma malha de controle com realimentação de saída. Além da adição desta ação integral, uma mudança de coordenadas será aplicada ao sistema, onde será garantido que o único ponto de equilíbrio que garante erro nulo de seguimento está no interior da sua região de linearidade. Os efeitos da saturação no sistema serão considerados através de condições de setor modificadas, as quais introduzem novos graus de liberdade ao projeto. Em um primeiro momento, a metodologia será aplicada para sistemas de tempo contínuo, considerando um esquema de controle conhecido como “integradores inteligentes”. Posteriormente, este esquema será simplificado, no que foi chamado de solução “clássica”. Além de apresentar um esquema de controle mais simples e um número menor de condições, estas condições são obtidas diretamente na forma de LMIs, evitando assim, a utilização de esquemas iterativos. Alguns problemas de otimização serão apresentados, podendo levar a três objetivos de controle distintos: maximização da referência admissível, maximização da condição inicial e maximização da perturbação admissível. Por meio de exemplos, será mostrado que esta solução apresenta resultados menos conservativos do que os apresentados na literatura corrente, além de chamar a atenção para um problema ignorado por outros autores. Este problema se refere à existência de pontos de equilíbrio dentro dos domínios de estabilidade mas fora da região linear, o que impossibilita a garantia de erro de seguimento nulo. Num segundo momento, esta metodologia será estendida para sistemas de tempo discreto. Mais uma vez, condições LMI serão obtidas a fim de projetar os controladores e oferecer estimativas dos domínios de estabilidade. Por não haver uma referência direta para comparação dos resultados, a metodologia será aplicada para exemplos estáveis, instáveis e com integradores, tanto no caso monovariável quanto no caso multivariável. Finalmente, será apresentado um estudo dos pontos de equilíbrio fora da região de linearidade, como mencionado anteriormente, considerando tanto sistemas de tempo contínuo quanto em tempo discreto. Este estudo será realizado para alguns tipos de sistemas, considerando apenas o caso monovariável. Será provado que estes equilíbrios só são possíveis em plantas assintoticamente estáveis, exigindo a consideração de uma condição extra na solução do problema de otimização. / This work addresses the problem of tracking constant references for linear systems subject to control saturation. The main idea is to present LMI conditions in order to design both a stabilizing controller and an anti-windup gain. These conditions ensure that the trajectories of the closed-loop system are bounded by an invariant ellipsoidal set, provided that the initial conditions are taken in this set and the references and the disturbances belong to a certain admissible set. The constant reference tracking and constant disturbance rejection is taken into account by the internal model principle, i. e., considering the introduction of an integral action in a unitary output feedback scheme. We also introduce the error co-ordinate representation, where is proved that there exists only one equilibrium point inside the linearity region and that this equilibrium point ensures perfect reference tracking. In order to consider the saturation effects, we use a modified sector condition, introducing new degrees of freedom to the synthesis problem. In a first step, the proposed framework was applied to the control scheme called “intelligent integrators”, regarding continuous-time systems. However, this control scheme does not allow the simultaneous synthesis so it is simplified to the so called “classical” anti-windup scheme. Based on this simplified control structure, LMI conditions are directly derived, avoiding therefore the necessity of applying iterative schemes. Convex optimization problems aiming at the maximization of the invariant set of admissible states and/or the maximization of the set of admissible references/disturbances are proposed. We show, by means of an example, that the obtained results are less conservative than the ones previously presented in related works. In these examples, we also show that a study about the existence of other equilibria inside the invariant set is worthwhile. Later, the proposed framework is extended to discrete-time systems, where new LMI conditions are presented in order to synthesize the controller and present an estimate of the stability domains. Due to a lack of related works, our framework is applied to stable, unstable and integrator examples. These examples consider both single and multi-variable systems. Finally, we conclude this work with a study about the possibility of existence of other equilibria inside the invariant set. For the single-input case, we show that this is only possible if the open-loop system is asymptotically stable. In this case, in order to avoid convergence to these points, additional constraints on the admissible references to be tracked should be considered. It is worth to emphasize that such kind of analysis has not been performed in previous works.