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January  2009, 5(1): 153-159. doi: 10.3934/jimo.2009.5.153

$H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach

Honglei Xu 1, and  Kok Lay Teo 2,

1. 

Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
2. 

Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received  March 2008 Revised  November 2008 Published  December 2008

This paper studies $H_\infty$ optimal control problems for a class of impulsive dynamical systems with norm-bounded time-varying uncertainty. By using a linear matrix inequality approach, some sufficient conditions are established to ensure both internally asymptotical stability and $H_\infty$ optimal performance of the impulsive closed-loop system. Moreover, based on the stability criteria, a linear time-invariant stabilizing control law is designed. Finally, a numerical example is presented to illustrate the effectiveness of our results.
Keywords: impulsive systems., robust optimal control, $H_\infty$ control.
Mathematics Subject Classification: Primary: 93B52, 93B36; Secondary: 37N4.
Citation: Honglei Xu, Kok Lay Teo. $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach. Journal of Industrial & Management Optimization, 2009, 5 (1) : 153-159. doi: 10.3934/jimo.2009.5.153
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