Sliding mode control for uncertain Markovian jump systems with actuator faults based on state estimation

This paper proposes a novel sliding mode control for nonlinear Markovian jump systems subject to partial actuator failures. The unmeasurable system states and unknown dynamics of uncertainties and nonlinearities pose significant challenges to controller design. To address these issues, a state observer incorporating the control input is developed, followed by the construction of an integral sliding surface relying on the state estimates. The dynamics of the sliding mode are analysed using the equivalent control method, and sufficient conditions are established to ensure stochastic stability of the closed-loop system based on Lyapunov stability theory and linear matrix inequalities. Finite-time convergence of the state trajectories to the designed surface is guaranteed by the proposed method, which also ensures the system remains on the manifold. The effectiveness and practical performance of the proposed scheme are demonstrated through numerical examples.