Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer

This paper is concerned with the problems of composite disturbance-observer-based control (DOBC) and ℋ∞ℋ∞ control for Markovian jump systems with nonlinearity and multiple disturbances. Our aim is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control scheme by integrating the output of the disturbance observer with state-feedback control law, such that, the closed-loop system can be guaranteed to be stochastically stable, and different types of disturbances can be attenuated and rejected. By constructing a proper stochastic Lyapunov–Krasovskii functional, sufficient conditions for the existence of the desired observer and the state-feedback controller are established in terms of linear matrix inequalities (LMIs), which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the effectiveness of the proposed approaches.