Asynchronous finite-time _H∞ control for switched linear systems via mode-dependent dynamic state-feedback

This paper concerns the asynchronous finite-time _H∞ control problem for a class of switched linear systems with time-varying disturbances. The asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By using the Average Dwell Time (ADT) and Multiple Lyapunov Functions (MLFs) technologies, some sufficient conditions which can guarantee that the corresponding closed-loop system is finite-time bounded with a prescribed _H∞ performance index via asynchronously switched control, are derived for the switched linear systems. Unlike the traditional Lyapunov asymptotic stability, there is no requirement of negative definiteness (or semidefiniteness) on the derivative of Lyapunov-like function. Moreover, a set of mode-dependent dynamic state feedback controllers are designed. Finally, two examples are provided to verify the efficiency of the proposed method.