Mathematical Problems in Engineering 
Volume 8 (2002), Issue 2, Pages 123-133
doi:10.1080/10241230212910

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

E. K. Boukas,1 P. Shi,2 M. Karan,3 and C. Y. Kaya4

 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

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.