Robust fault estimation and proportional derivative fault tolerant control for a class of singular systems with interval time-varying delay and disturbance

This paper deals with observer-based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time-varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full-rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real-time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer-based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time-varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed-loop system, which optimizes the design scheme of the fault-tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations.