Functional Observer-based Asynchronous Composite Anti-Disturbance Control for Markov Jump Systems with Multiple Disturbances

Multiple disturbances under multi channels in Markov jump systems (MJSs) lead to the asynchronism between controller modes and system modes, thus restricting the control performance of systems. This paper investigates functional observer-based asynchronous composite anti-disturbance control for MJSs with matched and mismatched disturbances. First, a functional observer-based asynchronous composite integral sliding mode control with H_∞ performance index (ACISMC-H_∞) framework is proposed to reject the matched disturbance and attenuate the norm-bounded disturbance simultaneously. On the one hand, a functional observer based control is proposed to estimate partly unavailable states and the matched disturbance generated by an exogenous system and compensate the matched disturbance. Meanwhile, the parameters of the observer can be found directly. On the other hand, a novel ACISMC-H_∞ is designed to attenuate the norm-bounded mismatched disturbance and ensure that the system state trajectories can always stay on the sliding surface. Due to the asynchronism between system modes and controller modes, the hidden Markov model is employed to detect model information in controller design. Second, sufficient conditions are proposed to achieve the stochastic stability and satisfy H_∞ performance of closed-loop MJSs. It is worth noting that the functional observer directly estimates the linear function of exogenous system states, that is, the matched disturbance, which reduces the observer order and computational load. Finally, a numerical example is given to illustrate the effectiveness of our proposed method.