Observer-based $$H_{\infty }$$H∞ control for nonlinear Markovian jump systems with time-delay and input saturation

This paper focus on the problem of observer-based $$H_{\infty }$$H∞ control for uncertain nonlinear Markovian jump systems with time-delay and actuator saturation. A delay-dependent sufficient condition is proposed which guarantees that the uncertain nonlinear Markovian jump system with time-delay and input saturation is stochastically stable via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region and the design method of observer-based $$H_{\infty }$$H∞ controller are given by solving LMIs and convex optimization problems. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed method.