Mathematical Problems in Engineering
Volume 2004 (2004), Issue 4, Pages 333-345
doi:10.1155/S1024123X04402038
ℋ∞ constant gain state feedback stabilization of stochastic hybrid systems with Wiener process
1Département de Génie Mécanique, École Polytechnique de Montréal, P.O. Box 6079, Station “Centre-ville”, Montréal H3C 3A7, Québec, Canada
2Electrical Engineering Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Received 17 February 2004; Revised 11 June 2004
Copyright © 2004 E. K. Boukas and N. F. Al-Muthairi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper considers the stabilization problem of the class of continuous-time linear stochastic hybrid systems with Wiener process. The ℋ∞ state feedback stabilization problem is treated. A state feedback controller with constant gain that does not require access to the system mode is designed. LMI-based conditions are developed to design the state feedback controller with constant gain that stochastically stabilizes the studied class of systems and, at the same time, achieve 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.