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IMA Journal of Mathematical Control and Information Advance Access published online on March 17, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl004
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received December 15, 2004
Accepted January 25, 2006

Article

{Hscript}{infty}stabilization of stochastic hybrid systems with white noise

E. K. Boukas 1 *

1 Mechanical Engineering Department, École Polytechnique de Montréal, PO Box 6079, Station Centre-ville, Montréal, Québec, Canada H3C 3A7

* To whom correspondence should be addressed.
E. K. Boukas, E-mail: el-kebir.boukas{at}polymtl.ca


  Abstract

This paper deals with the class of continuous-time linear stochastic hybrid systems with white noise. The {Hscript}{infty} stochastic stabilization problem is treated. LMI-based (Linear Matrix Inequality) conditions are developed to design the state feedback controller that stochastically stabilizes the studied class of systems and at the same time rejects the disturbance rejection of a desired level. The minimum disturbance rejection is also determined. Numerical examples are given to show the usefulness of the proposed results.

Keywords: stochastic systems; stabilization; LMI; {Hscript}{infty}-stabilization.
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