H_∞ Control Based on Game Theory Approach for Markov Jump Linear Systems

A game approach to H_∞robust control for Markov jump linear systems with ( x , u , v )-dependent noise described by an Itô-type equation is presented. By viewing the control variable u (t) and stochastic disturbance v (t) of the system as one player and the other player respectively, the H_∞ robust control problem is transformed into a two-person zero-sum differential game model. Moreover, by solving this differential game, it is proved that the existence condition of the H_∞ robust control strategy is equivalent to the solvability of the associated Riccati equation, and the explicit formula of the H_∞ robust control strategy is obtained. Finally, a numeric example is given to prove its feasibility.