L2 - L∞ Analysis and Control to Markov Jump Systems with Multiplicative Noise

In this paper, the L-2 - L-infinity control problem for a class of Markov jump systems with multiplicative noise was studied. A sufficient condition for the stochastic nonlinear Markov jump system to be asymptotically mean-square stable with a L-2 - L-infinity performance gain. is established in terms of Hamilton Jacabo inequalities (HJI). Based on the proposed sufficient condition, a state feedback controller is designed such that the closed-loop system satisfies the prescribed L-2 - L-infinity performance level. This paper also gives a sufficient condition for a linear Markov jump system to be asymptotically mean-square stable with prescribed L-2 - L-infinity performance by means of linear matrix inequalities (LMI). A method to design a state feedback controller is established. An example is given to illustrate the effectiveness of the proposed method.