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 $\gamma$ level of passivity performance. Finally, the feasibility and effectiveness of the proposed control scheme are verified by two examples.

本文研究了一类非线性离散时间奇异马尔可夫跳跃系统（DSMJS）在匹配不确定性、外部干扰和执行器故障信号下的基于被动的异步容错控制问题。系统状态一般无法测量，实际中可能会出现系统模式与控制器模式不同步的现象。我们特别关心的是为所考虑的复杂系统设计一种基于异步观测器的滑模控制 (SMC) 定律。首先，建立一个观测器来估计系统的未测量状态。其次，基于估计的状态，设计了依赖于模态的滑模面函数。而且，合成了一个基于异步自适应观测器的 SMC，以将系统轨迹驱动到指定的滑动表面上，并完全补偿执行器故障和 DSMJS 参数不确定性的影响。开发了足够的条件来识别滑动函数参数并保证闭环系统是随机可接受的$\gamma$被动性能水平。最后，通过两个算例验证了所提出控制方案的可行性和有效性。