L2 - L∞ analysis and control to Markov jump systems with multiplicative noise

In this paper, the L₂ - L_∞ 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 L₂ - L_∞ performance gain 7 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 L₂ - L_∞ performance level. This paper also gives a sufficient condition for a linear Markov jump system to be asymptotically mean-square stable with prescribed L₂ - L_∞ 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.