Abstract
This paper is concerned with the problem of $$H_{\infty }$$ control for a class of uncertain switched singular systems with time-varying state delays under asynchronous switching. The asynchronous phenomenon is caused by the choice of controller lagging behind the corresponding subsystem in practice. First, sufficient conditions by finding a novel piecewise Lyapunov–Krasovskii function combining with average dwell time technique are given to guarantee the exponential admissibility of the system. The algebraic equations and differential equations of the original system are proved to be exponentially stable. Then, a condition guaranteeing the $$H_{\infty }$$ performance of the original system is derived based on the above analysis. Furthermore, strict LMI formulas for solving the state feedback controller are given. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.
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