Abstract
AbstractIn this chapter, the problems of exponential stability and \(\mathscr {L}_1\)-gain analysis for positive time-delay Markov jump systems (MJSs) with switching transition rates are addressed. Another set of useful regime-switching model that is an extension of fixed transition rate to time-varying transition rate has been given. By resorting to the multiple linear co-positive Lyapunov function and average dwell time, sufficient conditions for exponential stability are proposed in standard linear programming. Based on the obtained results, \(\mathscr {L}_1\)-gain performance is analyzed. Finally, an example illustrates the validity of the main results.
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