Improved approach for passive stability of discrete-time Markovian jump linear systems via mode-dependent time-delayed controllers

In this paper, we investigate the problem of passive stability for discrete-time Markovian jump linear systems via mode-dependent time-delayed controllers by employing an improved free-weighting matrix approach. A Markov process as discrete-time, discrete-state Markov process is considered. First, a new result of mode-dependent stability analysis is first established for error systems without ignoring any terms in the derivative of Lyapunov-Krasovskii function by considering the relationship between the time-varying delay and its upper bound. Then, the delay-dependent passivity criterion is provided and a mode-dependent time-delayed controller is designed in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method.