H∞ State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the $H∞$ control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.