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Research Papers

# $H∞$ State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

[+] Author and Article Information
Ji Huang

e-mail: jihuang@uvic.ca

Yang Shi

e-mail: yshi@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055, STN CSC,

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received February 2, 2012; final manuscript received March 1, 2013; published online May 21, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 135(4), 041012 (May 21, 2013) (8 pages) Paper No: DS-12-1044; doi: 10.1115/1.4024009 History: Received February 02, 2012; Revised March 01, 2013

## Abstract

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the $H∞$ control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.

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## Figures

Fig. 1

The relation of jump linear systems, S-MJLSs, and MJLSs

Fig. 2

The state trajectories of the closed-loop S-MJLS using the proposed controller in Eq. (25)

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