Mean square exponential stability with l2−l∞ gain of discrete-time switched-Markovian jump systems

In this paper, the problem of mean square exponential stability with l 2 − l ∞ gain is studied for the discrete-time switched-Markovian jump systems, which are composed of a deterministic switched system and a Markovian jump system. The mode-dependent average dwell time method is adopted to design the switching signal for the deterministic switched system, and the Markovian jump property is presented by the Markov chain, which is dependent on the designed mode-dependent average dwell time switching signal. The multiple discontinuous Lyapunov function is constructed to guarantee the mean square exponential stability and l 2 − l ∞ performance. Furthermore, a novel inequality is established to show the relationship between multiple discontinuous Lyapunov functions and disturbances to derive the l 2 − l ∞ performance. Finally, two numerical examples and a circuit system are given to demonstrate the effectiveness of the obtained results.