Abstract
This paper is concerned with the problem of $$H_{\infty }$$ control for a class of switched systems. Time delays that appear in both the state and the output are considered. In addition, the switching of the controllers experiences a time delay with respect to that of subsystems, which is called “asynchronous switching.” By the utilization of the piecewise Lyapunov function technique, sufficient conditions that ensure the exponential stability and a weighted $$H_{\infty }$$ performance level for the closed-loop system under a mode-dependent average dwell time (MDADT) scheme is proposed. MDADT means that each subsystem has its own average dwell time (ADT), which is more general than ADT. Two types of MDADT are gained by dividing all the subsystems into two parts. Then, the asynchronous $$H_{\infty }$$ dynamical output feedback controller is designed in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.
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