This thesis studies the control algorithms used by a team of ECAVs (Electronic Combat Air Vehicle) to deceive a network of radars to detect a phantom track. Each ECAV has the electronic capability of intercepting the radar waves, and introducing an appropriate time delay before transmitting it back, and deceiving the radar into seeing a spurious target beyond its actual position. On the other hand, to avoid the errors and increase the reliability, have a complete coverage in various atmosphere conditions, and confronting the effort of the belligerent intruders to delude the sentinel and enter the area usually a network of radars are deployed to guard the region. However, a team of cooperating ECAVs could exploit this arrangement and plans their trajectories in a way all the radars in the network vouch for seeing a single and coherent spurious track of a phantom. Since each station in the network confirms the other, the phantom track is considered valid. This problem serves as a motivating example in trajectory planning for the multi-agent system in highly constrained operation conditions. The given control command to each agent should be a viable one in the agent limited capabilities, and also drives it in a cumulative action to keep the formation. In this thesis, three different approaches to devise a trajectory for each agent is studied, and the difficulties for deploying each one are addressed. In the first one, a command center has all information about the state of the agents, and in every step decides about the control each agent should apply. This method is very effective and robust, but needs a reliable communication. In the second method, each agent decides on its own control, and the members of the group just communicate and agree on the range of control they like to apply on the phantom. Although in this method much less data needs to communicate between the agents, it is very sensitive to the disturbances and miscalculations, and could be easily fell apart or come to a state with no feasible solution to continue. In the third method a differential geometric approach to the problem is studied. This method has a very strong backbone, and minimizes the communication needed to a binary one. However, less data provided to the agents about the system, more sensitive and infirm the system is when it faced with imperfectionalities. In this thesis, an object oriented program is developed in the Matlab software area to simulate all these three control strategies in a scalable fashion. Object oriented programming is a naturally suitable method to simulate a multi-agent system. It gives the flexibility to make the code more iv close to a real scenario with defining each agent as a separated and independent identity. The main objective is to understand the nature of the constrained dynamic problems, and examine various solutions in different situations. Using the flexibility of this code, we could simulate several scenarios, and incorporate various conditions on the system. Also, we could have a close look at each agent to observe its behavior in these situations. In this way we will gain a good insight of the system which could be used in designing of the agents for specific missions.

Orientador: Paulo Ricardo da Silva / Banca: João Carlos da Rocha Medrado / Banca: Fernando de Osório Mello / Banca: Claudio Aguinaldo Buzzi / Banca: Vanderlei Minori Horita / Resumo: Neste trabalho estudamos sistemas diferenciais forçados, também conhecidos como sistemas de equações com impasse. Estudamos os casos onde tais sistemas são suaves e os casos onde são possivelmente descontínuos. Usando técnicas de perturbação singular obtemos alguns resultados sobre a dinâmica destes sistemas em vizinhanças dos conjuntos de impasse. No caso suave, a Teoria de Fenichel clássica e crucial para o desenvolvimento dos principais resultados. Para o caso com descontinuidades, uma teoria similar a Teoria de Fenichel 'e desenvolvida. Além disso, estudamos a bifurcação de ciclos limites das órbitas periódicas de um centro diferencial linear quando perturbamos tal centro dentro de uma classe de sistemas diferenciais lineares por partes com impasse / Abstract: In this work we study constrained differential systems, also known as systems of equations with impasse. We study the cases where such systems are smo oth and the cases where they are p ossibly discontinuous. Using singular p erturbation techniques we obtain some results on the dynamic of these systems in neighb orho o ds of the impasse sets. In smo oth case, the classical Fenichel's Theory is crucial for the development of the main results. For the case with discontinuity, a similar theory to Fenichel's Theory is develop ed. Moreover, we study the bifurcation of limit cycles from the p erio dic orbits of a linear differential center when we p erturb such center inside a class of piecewise linear differential systems with impasse / Doutor

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-29T14:01:29Z No. of bitstreams: 1 genaropablozamudiochauca.pdf: 295489 bytes, checksum: 18212d3cbd798de7a3d5a0a546393c3c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-29T19:44:50Z (GMT) No. of bitstreams: 1 genaropablozamudiochauca.pdf: 295489 bytes, checksum: 18212d3cbd798de7a3d5a0a546393c3c (MD5) / Made available in DSpace on 2017-05-29T19:44:50Z (GMT). No. of bitstreams: 1 genaropablozamudiochauca.pdf: 295489 bytes, checksum: 18212d3cbd798de7a3d5a0a546393c3c (MD5) Previous issue date: 2012-03-29 / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / Em este trabalho estudamos algumas estruturas matemáticas presentes no modelo semiclássico para o spin não relativístico proposto nas referências [5] e [6]. Obtemos as equações semiclássicas de movimento para o spin não relativístico aplicando o teorema de Ehrenfest à equação de Pauli. Olhando o spin S como um momento angular interno, identicamos ele como a aplicação de momento ligada à ação de Poisson de SO(3) sobre o espaço de fase interno R6. Para eliminar os graus de liberdade extras presentes no modelo restringimos a dinâmica a uma superfície de spin V3 impondo vínculos. Além disso, mostramos que a superfície de spin V3 tem estrutura de fibrado com base S2, fibra típica SO(2) e com aplicação de projeção S. Finalmente apresentamos a formulação do problema variacional para o modelo. / In this work we study some mathematical structures arising in a nonrelativistic spinningparticle model proposed in [5] and [6]. We obtain the semiclassical equations of motion from the Pauli equation via the Ehrenfest theorem. Looking for the spin S as an intrisic angular momentum, we identify it with the momentum map of the SO(3) Poisson action on the inner phase space R6. In order to eliminate the extra degrees of freedom, we impose some constraints which restrict the evolution of the system on the spin surface V3. We show that V3 is a fiber bundle with base S2, standard fiber SO(2) and projection S. Finally, we present the formulation of variational problem for the model.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-06-23T19:07:29Z No. of bitstreams: 2 Dissertação - Yovani Adolfo Villanueva Herrera - 2017.pdf: 1975075 bytes, checksum: 4226bb99e3c16dbc26f70e7f7208e2c1 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Rejected by Erika Demachki (erikademachki@gmail.com), reason: on 2017-06-29T18:25:12Z (GMT) / Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-06-29T18:25:47Z No. of bitstreams: 2 Dissertação - Yovani Adolfo Villanueva Herrera - 2017.pdf: 2011176 bytes, checksum: 4107b5d00ad34d3b4127265319a99868 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2017-06-29T18:28:16Z (GMT) No. of bitstreams: 2 Dissertação - Yovani Adolfo Villanueva Herrera - 2017.pdf: 2011176 bytes, checksum: 4107b5d00ad34d3b4127265319a99868 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-06-29T18:28:16Z (GMT). No. of bitstreams: 2 Dissertação - Yovani Adolfo Villanueva Herrera - 2017.pdf: 2011176 bytes, checksum: 4107b5d00ad34d3b4127265319a99868 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-05-30 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The subject of this work is the theory of normal forms of smooth vector fields of constrained systems (systems of non-linear differential-algebraic equations). In this study we introduce the qualitative theory of ordinary differential equations, with topics such as stability, structural stability, bifurcations, limit cycles and catastrophes of differential equations, and the functional singularity theory. The goal of this work is classify and normalize constrained systems, first of all from the local point of view, we'll show an idea of the global one and our final objective will be extend this theory to differenciable manifolds of dimension $n \geq 2$. / O tema deste trabalho é a teoria das formas normais de campos vetoriais suaves de sistemas forçados (sistemas de equações diferenciais-algébricas não lineares). Neste estudo entram a teoria qualitativa de equações diferenciais ordinárias, com tópicos como estabilidade, estabilidade estrutural, bifurcações, ciclos limite e catástrofes de equações diferenciais e a teoria das singularidades de funções. O objetivo do trabalho é a classificação e normalização dos sistemas forçados, primeiramente do ponto de vista local, mostraremos uma ideia da análise global e será nossa finalidade estender esta teoria para variedades diferenciáveis de dimensão $n \geq 2$.

Vision systems have become ubiquitous. They are used for traffic monitoring, elderly care, video conferencing, virtual reality, surveillance, smart rooms, home automation, sport games analysis, industrial safety, medical care etc. In most vision systems, the data coming from the visual sensor(s) is processed before transmission in order to save communication bandwidth or achieve higher frame rates. The type of data processing needs to be chosen carefully depending on the targeted application, and taking into account the available memory, computational power, energy resources and bandwidth constraints. In this dissertation, we investigate how a vision system should be built under practical constraints. First, this system should be intelligent, such that the right data is extracted from the video source. Second, when processing video data this intelligent vision system should know its own practical limitations, and should try to achieve the best possible output result that lies within its capabilities. We study and improve a wide range of vision systems for a variety of applications, which go together with different types of constraints. First, we present a modulo-PCM-based coding algorithm for applications that demand very low complexity coding and need to preserve some of the advantageous properties of PCM coding (direct processing, random access, rate scalability). Our modulo-PCM coding scheme combines three well-known, simple, source coding strategies: PCM, binning, and interpolative coding. The encoder first analyzes the signal statistics in a very simple way. Then, based on these signal statistics, the encoder simply discards a number of bits of each image sample. The modulo-PCM decoder recovers the removed bits of each sample by using its received bits and side information which is generated by interpolating previous decoded signals. Our algorithm is especially appropriate for image coding. / Morbee, M. (2011). Optimized information processing in resource-constrained vision systems. From low-complexity coding to smart sensor networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12126 / Palancia

La gyrocinétique est un modèle clef pour la microturbulence en physique des plasmas. Elle présente encore plusieurs difficultés, qui pourraient invalider ses équations. Ce rapport de thèse clarifie trois d'entre elles. Tout d'abord, une de des coordonnées causait des soucis, d'un point de vue tant physique que mathématique ; une coordonnée adéquate est introduite, qui dissipe les difficultés et explique les structures intrinsèques sous-jacentes. Ensuite, des relations de récurrence explicites sont obtenues pour tous les ordres du développement perturbatif. Enfin, en utilisant la structure hamiltonienne de la dynamique, le couplage plasma-champ électromagnétique est implémenté d'un façon plus adaptée, avec d'importantes conséquences sur les équations gyrocinétiques.Plusieurs autres résultats sont obtenus, e.g. sur l'origine de l'invariant adiabatique centre-guide, sur une transformation centre-guide minimale très efficace, ou sur un modèle hamiltonien intermédiaire entre Vlasov-Maxwell et la gyrocinétique, dont les caractéristiques de Vlasov contiennent à la fois la dynamique lente centre-guide et la dynamique rapide du gyro-angle. Diverses méthodes de réduction sont utilisées, développées ou introduites, e.g. une transformée de Lie du mouvement, un relèvement transférant les réductions de la dynamique des particules à la dynamique des champs, ou une troncature reliée à la fois à la théorie des contraintes de Dirac et à une projection sur une sous-algèbre. Outre la gyrocinétique, cela clarifie d'autres réductions hamiltoniennes en plasmas, e.g. pour une dynamique incompressible ou électrostatique, pour la MHD, ou pour des fermetures fluides avec tenseur de pression. / Gyrokinetics is a key model for plasma micro-turbulence. It still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, explicit induction relations are obtained to go arbitrary order in the perturbative expansion. Third, using the Hamiltonian structure of the dynamics, the coupling between the plasma and the electromagnetic field is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations. Several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding-center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetics, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a litfing method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to projections onto Lie-subalgebras. Besides gyrokinetics, this is useful to clarify other Hamiltonian reductions in plasma physics, e.g. for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including moments of order two.

Dans cette thèse nous développons des structures de supervision permettant de définir des consignes optimales pour des actionneurs thermiques, ainsi que des stratégies de commande appropriées pour le pilotage d’une pompe à chaleur (PAC). Pour répondre à ces objectifs, plusieurs étapes ont été réalisées :- Modélisation orientée commande d’une PAC réversible, des thermistances, et de l’environnement permettant de les lier à l’intérieur de l’habitacle. Des modèles physiques ont été définis et intégrés dans une plateforme du type Model-in-the-Loop pour permettre a posteriori la validation des stratégies de commande et d’optimisation. - Commande d’une PAC. La linéarisation du modèle de PAC autour de certains points de fonctionnement a permis le développement de la commande de l’actionneur principal. La structure de commande proposée permet de prendre en compte, en boucle fermée, des contraintes d’état et d’entrée du système. Les performances de cette structure ont été analysées en considérant successivement des régulateurs principaux de type PI et Hinf. Enfin, des algorithmes réalisant le pilotage d’un actionneur secondaire du système ont été également proposés. - Optimisation des actionneurs thermiques. L’utilisation combinée de thermistances et de la PAC présente des avantages en termes de réduction de la consommation énergétique et/ou du maintien de la puissance thermique demandée dans des conditions aux limites de fonctionnement. Le problème d’optimisation a été résolu en deux temps : des solutions hors-ligne ont été obtenues par résolution d’un problème mixte en nombre entier avec modèle prédictif, puis utilisées pour déduire des stratégies embarquables sur le véhicule. / Through this thesis we develop some strategies to define the optimal set points for thermal actuators, as well as an adequate control strategy for a heat pump. To this extent, different steps were carried out:- Control-oriented modeling of a reversible heat pump, thermistors, and the environment connecting these elements to the interior of the car’s cabin. Simplified but non-linear physical models were defined and used to build a Model-in-the-Loop platform, which would later be considered for the validation of the control and optimization strategies. - Control of a heat pump. The linearization of the heat pump model around some operating points was used to develop the control of the electric compressor, being the main actuator. The proposed control structure takes into account, in closed loop, input and state constraints. The performance of the structure was analyzed by using main controllers of PI and Hinf type. Lastly, some control algorithms were also proposed to control a second actuator of the system. - Thermal actuators optimization. Despite the high efficiency of the heat pump, the use of thermistors can be advantageous both for reducing the energetic consumption and/or to ensure the thermal power requests in extreme conditions. The optimization problem was carried out in two steps: offline solutions were firstly obtained solving a mixed-integer problem with predictive model, then used to derive some strategies that could be embedded in the vehicle.

<p>A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK.</p><p>Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics.</p><p>New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance.</p><p>Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK.</p><p>The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.</p>

A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK. Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics. New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance. Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK. The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.

Το αντικείμενο της διατριβής αφορά την ανάλυση και τον έλεγχο δυναμικών συστημάτων με περιορισμούς στο διάνυσμα της εισόδου ή/ και στις μεταβλητές κατάστασης. Τα θεωρητικά εργαλεία που χρησιμοποιήθηκαν για την εξαγωγή των αποτελεσμάτων προέρχονται από τη θεωρία ευστάθειας Lyapunov, την αρχή σύγκρισης συστημάτων και τη θεωρία συνόλων, και οδήγησαν στην εδραίωση συνθηκών ευστάθειας και την ανάπτυξη συστηματικών μεθόδων εύρεσης λύσης στο πρόβλημα ελέγχου συγκεκριμένων κατηγοριών δυναμικών συστημάτων με περιορισμούς. Πιο συγκεκριμένα, για την κατηγορία των γραμμικών συστημάτων συνεχούς και διακριτού χρόνου, προτάθηκε μια νέα μέθοδος επίλυσης του προβλήματος ευσταθειοποίησης συνόλου αρχικών συνθηκών και του υπολογισμού του μέγιστου θετικά αμετάβλητου ή αμετάβλητου με έλεγχο συνόλου παρουσία περιορισμών στις εισόδους ή/και στις καταστάσεις. Τα αποτελέσματα επεκτάθηκαν και στην κατηγορία των γραμμικών συστημάτων με πολυτοπικη αβεβαιότητα. Επίσης, μελετήθηκε η κατηγορία των αυτοανάδρομων μοντέλων κινούμενου μέσου όρου (ARMA models). Αρχικά εδραιώθηκαν συνθήκες που εγγυώνται ευστάθεια για ένα συγκεκριμένο σύνολο αρχικών συνθηκών παρουσία περιορισμών. Τα αποτελέσματα αυτά εφαρμόστηκαν στην κατηγορία των δικτυωμένων συστημάτων ελέγχου (NCS), όπου υπολογίστηκε ένας κοινός γραμμικός νόμος ελέγχου ανατροφοδότησης κατάστασης για όλο το εύρος της καθυστέρησης της εισόδου. Τέλος, μελετήθηκε η κατηγορία των διγραμμικών συστημάτων συνεχούς και διακριτού χρόνου. Αρχικά διατυπώθηκαν ικανές συνθήκες ύπαρξης πολυεδρικών συναρτήσεων Lyapunov για αυτήν την κατηγορία συστημάτων. Το πρόβλημα που μελετήθηκε είναι η ευσταθειοποίηση μιας συγκεκριμένης περιοχής του χώρου κατάστασης παρουσία περιορισμών στις εισόδους και τις καταστάσεις και προτάθηκε μια υποβέλτιστη λύση που οδηγεί στον υπολογισμό γραμμικού νόμου ελέγχου ανατροφοδότησης κατάστασης. Όλα τα αποτελέσματα προκύπτουν από την επιλογή πολυεδρικών συναρτήσεων Lyapunov οι οποίες οδηγούν στο χαρακτηρισμό πολυεδρικών εκτιμήσεων της περιοχής ελκτικότητας και θετικά αμετάβλητων συνόλων. Τα κυριότερα οφέλη της επιλογής τέτοιων συναρτήσεων είναι η μη συντηρητική εκτίμησης της περιοχή ευστάθειας και η εδράιωση συνθηκών που οδηγούν σε συστηματικές μεθόδους επίλυσης των προβλημάτων ανάλυσης και ελέγχου, η λύση των οποίων προκύπτει από τη λύση γραμμικών προβλημάτων βελτιστοποίησης. / This dissertation considers the problem of stability analysis and control of dynamical systems under constraints in the input and/or state vector. The theoretical tools used arise from Lyapunov stability theory, comparison systems theory and set theoretic methods and lead to the determination of stability conditions and development of systematic methods that solve the control problem of constrained systems of particular type. In specific, for linear discrete or continuous time systems, a novel method that leads to the solution of the initial condition set stabilization problem as well as the maximal controlled invariant set computation problem is presented. These results have been extended for the case of linear systems with polytopic uncertainty. Also, the category of auto regressive moving average (ARMA) models is investigated. First, conditions that guarantee stability for a preassigned initial conditions set for constrained ARMA models are established. These results are applied to the category of networked control systems (NCS), were a single linear state feedback control law is computed for the whole range of the input delay. Finally, the category of bilinear discrete-time or continuous-time systems is investigated. Initially, sufficient conditions which guarantee existence of polyhedral Lyapunov functions are presented. The problem studied here is the stabilization of an initial condition set in the presence of input and state constraints. The solution proposed is suboptimal and leads to the determination of a linear state feedback control law. The choice of Lyapunov functions leads to the determination of a polyhedral approximation of the domain of attraction as well as polyhedral positively invariant sets. The main benefits of choosing this type of functions is the nonconservative estimation of the domain of attraction and the establishment of stability conditions that lead to systematic control design methods through the solution of linear programming problems.