Sensor Fault Detection and Reliable Control of Singular Stochastic Systems with Time-Varying Delays

In unmanned systems, especially in large-scale and complex ones, sensor and communication failures occur from time to time and are hard to avoid. Therefore, this paper studies the fault detection problem of a class of unknown nonlinear singular uncertain time-varying delay Markov jump systems (UNSUTVDMJSs). Firstly, the corresponding sliding mode controller (SMC) is designed by using the equivalent control principle, and the unknown nonlinearity is equivalently replaced by changing the system input. Then, a fault detection filter adapted to this system is designed, thereby obtaining the unknown nonlinear stochastic singular uncertain Augmented filter residual system (UNSSUAFRS) model. To obtain the sufficient conditions for the random admissibility of this augmented system, a weak infinitesimal generator was used to design the required Lyapunov-Krasovskii functional. With the help of the Lyapunov principle and $H_{\infty }$ performance analysis method, the sufficient conditions for the random admissibility of UNSSUAFRS under the $H_{\infty }$ performance index $\gamma$ were derived. Finally, with the aid of the designed residual evaluation function and threshold, simulation analysis was conducted on the examples of DC servo motors and numerical calculation examples to verify the effectiveness and practicability of this fault detection filter.