Sampled-Data Control And Stability Analysis For Switched Systems

Switched systems, a special subclass of hybrid systems, are widely applied into the control engineering field and have been studied extensively in the control theory field. However, in real world applications, some inevitable reality factors are often neglected in the study of switched systems. For example, at switching instants, the mismatch problem between controller modes and system modes in switched sampled-data control systems, or the problem of instantaneous state jumps in switched singular systems may occur, which both may corrupt the switched system behavior. Therefore, in the thesis, these two practical issues have been deeply investigated. The main contents are as follows:The sampled-data control problem of switched linear systems with average dwell time is studied. Since the subsystem switching occurs during the sampling intervals while the associated controller is not switched, the asynchronous switching phenomena arise. A new class of functionals consisting of multiple Lyapunov functions and looped functionals are developed to present sufficient conditions on the exponential stability of sampled-data state-feedback and stabilization for such systems.The input-to-state stability problem of a class of switched nonlinear sampled-data control systems is investigated. By employing the Lyapunov functions approach, and under the average dwell time switching based on the hypothesis of the slow switching, sufficient conditions are obtained where the subsystems can be not input-to-state stable during asynchronous phase. Then, the results are extended to the case under arbitrary switching satisfying the average dwell time.Subjecting to state jumps, the stability problem of a class of switched singular systems constrained by the boundedness of states in the fixed time and the nonnegativity of all states is discussed. Firstly, the problem of finite-time stability for such systems is studied under two kinds of switching strategies. If the subsystems are finite time stable, an average dwell time condition is provided to guarantee the switched systems are finite time stable. Otherwise, the state-dependent switching law is designed to stabilize the switched system in a finite time, even if no subsystem is finite time stable. Secondly, based on the equivalent switched impulse system and the properties of the projector matrix, the stability problem for a class of switched positive singular systems with average dwell time switching are investigated.