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Mathematical Problems in Engineering
Volume 8, Issue 2, Pages 123-133
http://dx.doi.org/10.1080/10241230212910

Linear discrete-time systems with Markovian jumps and mode dependent time-delay: Stability and stabilizability

1Mechanical Engineering Département, École Polytechnique de Montréal, P.O. Box 6079, Station, “centre-ville”, Montréal H3C 3A7, Québec, Canada
2Land Operations Division, Defence Science and Technology Organisation, P.O. Box 1500, Salisbury 5108, SA, Australia
3CRC for Sensor Signal and Information Processing (CSSIP), SPRI Building, Technology Park, Mawson Lakes, 5095, SA, Australia
4School of Mathematics, University of South Australia, Mawson Lakes, 5095, SA, Australia

Received 7 August 2001; Revised 21 January 2002

Copyright © 2002 Hindawi Publishing Corporation. 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 stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI) techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.