Passivity-based asynchronous fault-tolerant control for nonlinear discrete-time singular markovian jump systems: A sliding-mode approach

Abstract

This paper deals with the problem of passivity-based asynchronous fault-tolerant control for a class of non-linear discrete-time singular Markovian jump systems (DSMJSs) subjected to matched uncertainties, external disturbance, and actuator faulty signals. The system’s states are generally unavailable for measurement, and the asynchronous phenomenon between the system and controller modes may occur in practice. Our particular concern is to design an asynchronous observer-based sliding mode control (SMC) law for the considered complex system. Firstly, an observer is established for the estimation of the unmeasured states of the system. Secondly, based on the estimated states, a mode-dependent sliding mode surface function is designed. Moreover, an asynchronous adaptive observer-based SMC is synthesized to drive the system trajectories onto the specified sliding surface and completely compensate for the effects of actuator faults and parameter uncertainties of the DSMJSs. Sufficient conditions are developed to identify the sliding function parameters and to guarantee that the closed-loop system is stochastically admissible with a γ level of passivity performance. Finally, the feasibility and effectiveness of the proposed control scheme are verified by two examples.