Finite‐time analysis and design for discrete‐time switching dynamics Markovian jump linear systems with time‐varying delay

Abstract

The problems of finite-time analysis and design for a class of discrete-time switching dynamics Markovian jump linear systems (SD-MJLSs) with time-varying delay are investigated in this study. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition probability matrix, which is subject to a high-level average dwell time (ADT) switching. The time delay is considered as time varying and has a lower and upper bound. First, sufficient conditions, which guarantee the stochastic finite-time boundedness of the underlying systems, are presented by employing the ADT approach. These conditions are not only dependent on the delay upper bound but also the delay range. Then, a finite-time weighted l 2 gain of such delay SD-MJLSs is obtained to measure the disturbance attenuation capability over a fixed time interval and the design of the stabilising controller is further given. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. Finally, a numerical example is given to verify the potential of the developed results.