Fault-tolerant control for almost periodic piecewise time-varying systems with variable periods

This paper investigates the fault-tolerant control problem for a class of almost periodic piecewise time-varying systems (APPTVSs) with variable periods. The system model accounts for two practical factors: variations in system periods within a bounded interval and actuator failures. Based on this consideration, a constructive fault-tolerant control approach is established for such systems. Stability analysis is performed for the considered APPTVS, and sufficient conditions are derived to ensure the exponential stability of the closed-loop system. By employing a matrix polynomial approach to decouple products of time-varying terms, we transform the synthesis of the corresponding fault-tolerant controller into a convex optimization formulation. A design that provides enhanced flexibility for almost periodic controller gains is obtained by selecting tunable parameters for subinterval partitioning. Through numerical simulations of single-input and multiple-input APPTVSs, it is verified that the designed controllers ensure exponential stability of the closed-loop system under actuator faults while preserving almost periodicity, thereby demonstrating the effectiveness of the proposed approach.