Mean Square Exponential l₂ – l∞ Control of Switched-Markovian Jump Systems With Edge-Dependent Transition Probability

In this study, the problem of mean square exponential $l_{2}-l_{\infty }$ control is investigated for switched-Markovian jump systems (SMJSs). SMJSs are subject to deterministic switching obeying mode-dependent average dwell time (MDADT) and stochastic switching complying to Markov chain. mode-dependent transition probability (MDTP) and edge-dependent transition probability (EDTP) are proposed. MDTP describes the transition probability (TP) of Markovian jump systems (MJSs) under deterministic switching, and EDTP portrays the TP among MJSs affected by deterministic switching, which is associated with two different deterministic switching modes. Using multiple discontinuous Lyapunov function technology, the mean square exponential stability with $l_{2}-l_{\infty }$ performance is guaranteed by the MDADT method, MDTP and EDTP. Certain solvable sufficient conditions are obtained for the controller. Finally, two numerical examples and a practical example are provided to illustrate the validity of the obtained results.