# American Institute of Mathematical Sciences

May  2005, 5(2): 365-384. doi: 10.3934/dcdsb.2005.5.365

## $H_\infty$ and robust control of interconnected systems with Markovian jump parameters

 1 College of Engineering, UAE University, P0 Box 17555 Al-Ain, United Arab Emirates 2 School of Technology, University of Glamorgan, Pontypridd, Wales, CF37 1DL, United Kingdom 3 School of Information Science, Kyushu Tokai University, 9-1-1, Toroku, Kumamoto 862-8652, Japan

Received  September 2003 Revised  April 2004 Published  February 2005

In this paper, we examine the problems of stochastic stability and stabilization for a class of interconnected systems with Markovian jump parameters. The jumping parameters are treated as continuous-time, discrete- state Markov process. The purpose is to design a decentralized state feedback controller such that stochastic stability and a prescribed $H_\infty$-performance are guaranteed. Next, the robust $H_\infty$-control problem for linear interconnected systems with Markovian jump parameters and parametric uncertainties is studied. The parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state matrix. Both cases of finite-horizon and infinite-horizon are analyzed. We establish that the decentralized control problem for interconnected Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled differential (or algebraic) Riccati equations. Extension of the developed results to the case of uncertain jumping rates is provided.
Citation: M. S. Mahmoud, P. Shi, Y. Shi. $H_\infty$ and robust control of interconnected systems with Markovian jump parameters. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 365-384. doi: 10.3934/dcdsb.2005.5.365
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