Model reduction for discrete-time Markov jump Lur׳e systems with time-varying delays in a unified framework. Issue 11 (November 2015)

• Record Type: Journal Article
• Authors: Zhang, Yujie; Ou, Yongsheng
• Is Part Of: Journal of the Franklin Institute. Volume 352:Issue 11(2015:Nov.)
• Page Start: 5003
• Page End: 5023
• Publication Date: 2015-11
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2015.08.006
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: 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 ∞, l 2 – 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. Abstract : Highlights: The extended dissipative performance is introduced to Markov jump Lur'e systems. A reduced-order Markov jump linear system is obtained under a unified framework. A Lyapunov–Krasovskii function with the sector condition assumption is used.