Passivity and passification for switching Markovian jump systems with time-varying delay and generally uncertain transition rates

This study deals with the problem of passivity and passification for switching Markovian jump systems with timevarying delay and generally uncertain transition rates. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition rate matrix, which is subject to a high level average dwell time switching. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. The generally uncertain transition rates cover uncertain transition rates and partly known transition rates as two special cases. First, sufficient conditions, which guarantee the exponential mean-square stability and stochastic passivity of the underlying systems, are presented by resorting to average dwell time approach. Second, the design of the stabilising controller is given further. Moreover, an improved controller design method, which could provide efficiency and practicability is further developed. All the proposed conditions are given in the form of linear matrix inequalities. Finally, practical examples illustrate the validity of the obtained results.