Composite anti‐disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances

Summary In this paper, the problem of composite anti‐disturbance resilient control is studied for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. The multiple disturbances include two types: one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L 2 [0, ∞ ). The first class of disturbances is estimated by designing a disturbance observer. Combining the disturbance estimation with conventional L 2 − L ∞ resilient control law, a composite anti‐disturbance control scheme is constructed such that the closed‐loop system is stochastically stable, and different types of disturbances can be attenuated and rejected. By using Lyapunov function method and linear matrix inequalities technique, some sufficient conditions for the desired controller and observer gains are developed. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.