Infinite horizon H∞H∞ control for nonlinear stochastic Markov jump systems with (x,u,v)(x,u,v)-dependent noise via fuzzy approach

In this paper, the H∞H∞ control problem is studied for nonlinear stochastic Markov jump systems with state, control and external disturbance-dependent noise ((x,u,v)(x,u,v)-dependent noise for short). A sufficient condition is derived for the infinite horizon H∞H∞ control of such systems in terms of a set of coupled second-order Hamilton–Jacobi inequalities (HJIs). In general, it is difficult to solve these coupled HJIs. By using fuzzy approach, the infinite horizon H∞H∞ control design for nonlinear stochastic Markov jump systems is developed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Two numerical examples are presented to illustrate the effectiveness of the proposed design methods.