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

摘要

This paper addresses the model reduction problem for a class of Markov jump Lure systems with piecewise homogeneous transition probabilities and time-varying delays in discrete-time domain. The purpose of this paper is to solve the H-infinity, l(2)-l(infinity), 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. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.