Analysis And Controller Design For Switched Hybrid Dynamical Systems

As an important class of hybrid dynamical systems, a switched system is composed of several continuous-time sub-systems or discrete-time subsystems and the switching signals among them. With its own particularity, it is different form the traditional continuous-time systems or discrete-time systems. Due to the existence of the switching signal, its dynamics may become very complicated, for example, the state trajectory may jump at the switching point, its stability may change. Hence, it is very important to how to choose the proper switching signal. During the last three decades of so, there is an increasing interest on the modeling, analysis, synthesis, and control of witched systems. Nowadays more and more people have paid attention to the stability analysis of the switched systems and the study of the switching control.This dissertation devotes on the study of the linear uncertain switched systems and time-delay systems, including the design of the feedback controllers and the switching signals, the globally asymptotical stability and the exponential stability of the closed-loop systems. The main contributions of the research work presented in this dissertation are as follows:1. In the first part, the robust exponential stability of a class of discrete time impulsive switched systems with structure perturbations is studied. The given switched systems are composed of stable subsystems and unstable subsystems. Based on the average dwell time concept and by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, it is shown that if the average dwell time and the ratio of the activation time with stable subsystems to the activation time with unstable subsystems are properly large, the given switched system is robustly exponentially stable with a desired stability margin. Compared with the traditional Lyapunov methods, our layout is more clear and easy to carry out.2. In the second part, the exponential stability is considered for continuous time switched systems containing both stable and unstable subsystems with state jump and structure perturbations. By utilizing the matrix measure concept and the average dwell-time approach, it is shown that if the average dwell-time and the ratio of the total activation time of the subsystems with negative matrix measure to the totalactivation time of the subsystems with nonnegative matrix measure are both chosen appropriately large, the exponential stability of a desired degree is guaranteed. The main contribution of this part is that a feasible algorithm on the exponential stability study of the switched systems is proposed.3. In the third part, the robust quadratic stabilization problem and asymptotic stabilization problem are analysized for discrete time switched dynamical systems with nonlinear perturbations, which satisfy the matching condition. The robust state feedback controllers and output feedback controllers are designed respectively using common Lyapunov function technique and multiple Lyapunov function technique. Also the asymptotical stabilization switching laws are presented. The designed controllers and switching signals guarantee the quadratic stability and asymptotic stability.4. In the forth part, we go on studying the robust stabilization problem for discrete time switched systems. Here we consider the stabilization problem of structure perturbed uncertain discrete time switched systems. Robust state feedback controllers and output feedback controllers are designed respectively using common Lyapunov function technique and multiple Lyapunov function technique. Additionally, the asymptotical stabilization switching laws are presented, which guarantee the quadratic stability and asymptotic stability of the closed-loop switched systems.5. In the fifth part, the robust state feedback stabilization problem is investigated for continuous time switched systems with structure perturbations and nonlinear disturbances. The nonlinear disturbances include the uncertainty satisfying matching condition and the one not satisfying the matching condition. The problems of quadratic stabilization and asymptotic stabilization are considered for the given uncertain switched systems. Based on the common Lyapunov function technique, several sufficient conditions for the robust stability of the switched systems are presented in the form of matrix inequalities. The simulations validate the effectiveness of the main algorithm. The work in this part forwards the study in the previous two parts.6. In the sixth part, the robust static output feedback stabilization problem and robust dynamic output feedback stabilization problem are analyzed for a class of discrete-time switched systems with state delays and nonlinear perturbations. By utilizing Schur complement formula and the related notion of LMI, a series of sufficient conditions are presented, which guarantee the robustly globally uniformlyasymptotic stability of the closed-loop switched system. Additionally, the problem of the maximal nonlinear bound when the closed-loop switched system is asymptotically stable is also studied. As we pointed out, this problem can be solved by judging the feasibility of one convex optimization. All the results are given in linear matrix inequality form. The simplicity of the design algorithm makes it easy to carry out.