Model reduction for discrete-time Markov jump Lur׳e systems with time-varying delays in a unified framework

This paper addresses the model reduction problem for a class of Markov jump Lur׳e systems with piecewise homogeneous transition probabilities and time-varying delays in discrete-time domain. The purpose of this paper is to solve the H∞, l2-l∞, passivity and dissipativity model reduction problems in discrete-time domain in a unified framework by using an extended dissipativity performance index. By constructing a mode-dependent Lyapunov-Krasovskii functional with the sector condition assumption for the nonlinearities, the sufficient conditions on the existence of desired reduced-order models are derived in terms of linear matrix inequalities, which ensures that the resulting error system is stochastically stable and has a prescribed performance index. A numerical example is presented to show the effectiveness of the proposed theories.