Abstract:
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.