Stabilization And Tracking Control For Switched Systems Under Asynchronous Switching

Switched systems are pervasive in engineering applications. In recent years, switched systems have been studied deeply, and many remarkable achievements have been obtained. For the control problem of switched systems, it is generally assumed that the switching of the controllers is matched with that of the subsystems, i.e., they are activated synchronously at switching instant. In practical engineering, however, since it inevitably takes some time to identify the active subsystem and apply for the matched controller, the switching time of controllers may lag behind that of the corresponding subsystems, which results in asynchronous switching. This phenomenon is harmful for pursuing good performance and even destabilizes the systems. Hence, it is necessary and significant to study this problem. Stabilization and tracking control problems for switched systems under asynchronous switching have been investigated in this thesis, the main contents including:The stabilization problem for a class of stochastic neutral switched systems under asynchronous switching is studied. The stability of switched systems under average dwell time switching signals is obtained. The new Lyapunov function constructed is dependent on the controllers’switching signal, which counteracts the difficulty of controller design under asynchronous switching. The results presented allow the subsystems to be unstable during asynchronous phase.Sliding mode variable structure control strategy is proposed to solve the stabilization problem for a class of uncertain nonlinear stochastic switched systems under asynchronous switching. The integral sliding surface is constructed, which eliminates the reaching process and thus improves robustness. The variable structure controllers are designed to force the systems to remain in the sliding motion, and the results are presented to guarantee the mean-square exponential stability of switched systems under asynchronous switching. Then, the results for nonlinear cascaded switched systems composed of linear and nonlinear switched systems are extended to nonlinear switched systems with two cascaded nonlinear parts.The output tracking control problem for switched systems under asynchronous switching is investigated. The controllers with the integral term of tracking error are designed to eliminate the steady-state tracking error effectively. The augmented systems composed of the given switched systems and tracking error systems are constructed. By analyzing the stability of the augmented systems in matched and mismatched periods, the stability and the robust H∞tracking performance of switched systems are obtained.