Robust Stability and Stabilizability of Jump Linear Uncertain Systems With Time Delay

Abstract

In chapter 8, we dealt with the class of time delay systems with Markov jumps, and we developed results for stability and the stabilizability problems. The dynamic was assumed to be free of uncertainties. But since in practice uncertainties cannot be neglected, this chapter deals with the robust stability and stabilizability of the class of linear uncertain system with Markov jumps and time delay. For this purpose, consider a hybrid system withNmodes, that isS ={1, 2, • • •, N}. Mode switching is governed by a continuous-time Markov process {r_tt> 0} as defined previously.