Self-Triggered Fault-Tolerant Control of Cyber-Physical Markovian Jump Systems via Descriptor Sliding-Mode Observer

This paper investigates fault-tolerant control of cyber-physical Markovian jump systems, which represent a broad class of industrial cyber-physical systems (ICPS) operating under multiple modes and heterogeneous uncertainties. A descriptor sliding-mode observer is first developed to synchronously reconstruct system states, actuator faults, sensor faults, and exogenous disturbances in real time. Based on the reconstructed variables, a novel self-triggered fault-tolerant control mechanism is then designed on the actuator side to alleviate the cyber communication burden in network-constrained ICPS. Sufficient conditions are established to guarantee the stochastic stability of both the closed-loop system and the estimation error, enabling a co-design framework for the observer, controller, and triggering logic via convex programming. Simulation results on a single-link flexible joint robot demonstrate that the proposed approach achieves fast and accurate fault and disturbance reconstruction, with estimation errors converging within a few seconds under stochastic mode switching. Moreover, the self-triggered communication scheme reduces the number of control signal transmissions by approximately 65% compared with a conservative time-triggered strategy, while maintaining the desired closed-loop performance. These results verify the effectiveness of the proposed control and communication co-design framework at the algorithmic level for resource-constrained ICPS-oriented robotic systems.