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. Copyright © 2011 John Wiley & Sons, Ltd.

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