Uncertain Switched Systems, Robust Control

This dissertation devotes to the study of robust H_∞ control for the uncertain switched systems. The main contributions in this dissertation are as follows:1. In the first part, the problem of robust H_∞ state feedback stabilization for uncertain switched impulsive systems with state delay is studied. The system under consideration involves time delay, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. The nonlinear uncertainties meet with the linear growth condition. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust H_∞ disturbance attenuation performance in terms of certain linear matrix inequalities(LMIs). The robustly stabilizing state feedback H_∞ controller can be constructed by using the corresponding feasible solution of the linear matrix inequalities(LMIs). Finally, the effectiveness of the algorithms is illustrated with an example.2. In the second part, the problem of globally asymptotic stability analysis and globally asymptotic stabilization under arbitrary switching of uncertain discrete-time switched systems with state delay is considered. Looking at the existence of switched quadratic Lyapunov function, a necessary and sufficient condition has been presented to check the desired stability and stabilizability. The condition is presented in terms of linear matrix inequality(LMI) and does not depend on time delay. A suitable globally asymptotically stabilizing switched state feedback controller has also been given. Two numerical examples are presented to illustrate the effectiveness of the proposed algorithm.3. In the third part, the problem of the robust H_∞ state feedback control is investigated for a class of swiched systems with impulsive effects and parametric uncertainties. Using the switched Lyapunov function technique, some linear matrix inequality(LMI) based sufficient conditions and the robust H_∞ state feedback controller are proposed to guarantee the desired robust stability and robust H_∞ performance. Finally, a numerical example is given to illustrate the effectiveness of the main result.