Well-posedness of Bimodal State-based Switched Systems

AbstractIn this work, we consider the well-posedness of state-based switched systems in the sense of piecewise classical solutions which commonly arise in the control of hybrid systems. We give some necessary and sufficient conditions for the well-posedness of this class of systems. These results can be used as tools for excluding the bimodal system having a Zeno state

Robust Stabilization of Nonlinear Systems by Quantized and Ternary Control

Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by quantized and ternary controllers and apply them to some significant control problems.Comment: 14 pages, 4 figure

Control synthesis for dynamic switched systems

Orientador: Jose Claudio GeromelDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Neste trabalho, são propostas condições suficientes para a estabilidade assintótica de sistemas lineares, contínuos no tempo, com comutação que asseguram um custo garantido de desempenho. Estas condições dependem da solução de um conjunto de desigualdades de Lyapunov-Metzler, definidas em [Geromel & Colaneri, 2006], que possuem natureza não-convexa, sendo portanto, de difícil solução. Para contornar este problema, apresentamos condições de estabilidade mais conservadoras baseadas em uma subclasse de matrizes de Metzler com elementos iguais na diagonal principal, que podem ser resolvidas através de desigualdades matriciais lineares e busca unidimensional. Os resultados apresentados em [Geromel & Colaneri, 2006], que fornecem condições para a estabilidade de sistemas dinâmicos lineares com comutação, são generalizados para lidar com sistemas mais gerais, a saber, sistemas dinâmicos sujeitos a perturbações impulsivas. A proposta elaborada assegura a estabilidade assintótica inclusive na presença de possíveis modos deslizantesAbstract: In this work, sufficient conditions are proposed for the study of asymptotic stability of continuous time linear systems with commutation, which assure a guaranteed cost of performance. These conditions depend on the solution of a set of Lyapunov-Metzler inequalities, defined in [Geromel & Colaneri, 2006], which are difficult to solve due to their non-convex nature. However, to circumvent this difficulty, we present more conservative stability conditions based on a subclass of Metzler matrices characterized by having equal elements on the main diagonal. Although these conditions are more conservative, they can be solved by Linear Matrix Inequalities (LMls) and unidimensional search. The analysis done in [Geromel & Colaneri, 2006], which provides the stability conditions for linear dynamic systems with commutation is expanded to cover a more general class of systems with commutation and subject to impulsive disturbances. The conditions presented in this work assure the stability even in the presence of possible sliding modesMestradoAutomaçãoMestre em Engenharia Elétric

Stabilization by means of state space depending switching rules

In this paper we consider switched systems defined by a pair of linear systems $\dot x =A_1 x$, $\dot x =A_2 x$, such that there exists a neutrally stable linear combination of the matrices $A_1$, $A_2$. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense. The result is illustrated by some simulations and examples

Qualitative Studies of Nonlinear Hybrid Systems

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance. The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems. Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior. Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems. Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay. Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions. Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results