# American Institute of Mathematical Sciences

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

 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.
Citation: Honglei Xu, Kok Lay Teo. $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: An LMI approach. Journal of Industrial and Management Optimization, 2009, 5 (1) : 153-159. doi: 10.3934/jimo.2009.5.153
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