Mathematical Problems in Engineering
Volume 4 (1998), Issue 4, Pages 269-288

Design of robust controller for linear systems with Markovian jumping parameters

K. Benjelloun,1 E. K. Boukas,1 O. L. V. Costa,2 and P. Shi3

1Mechanical Engineering Department, École Polytechnique de Montréal, P.O. Box 6079, Station “Centre-Ville”, Montréal H3C 3A7, Que., Canada
2University of Sao Paulo, Department of Electronic Engineering, Sao Paulo 05508-900, SP, Brazil
3Centre for Industrial and Applicable Mathematics, The University of South Australia, SA 5095, Australia

Received 15 May 1997; Revised 11 August 1997

Copyright © 1998 K. Benjelloun et al. 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.


This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.