L2–L∞ fuzzy control for Markov jump systems with neutral time-delays

The L2–L∞ fuzzy control problem is considered for nonlinear stochastic Markov jump systems with neutral time-delays. By means of Takagi–Sugeno fuzzy models, the fuzzy controller systems and the overall closed-loop fuzzy dynamics are constructed. A sufficient condition is firstly established on the stochastic stability using stochastic Lyapunov–Krasovskii functional. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of mode-dependent state feedback L2–L∞ fuzzy controller are presented and proved respectively for constant and time varying case. Finally, the design problems are formulated as optimization algorithms. Simulation results are exploited to illustrate the effectiveness of the developed techniques.