Robust Fault-tolerant Control of Periodic Piecewise Time-varying Systems Based on Matrix Polynomials

This paper investigates the robust fault-tolerant control issue for a type of periodic piecewise time-varying systems (PPTVSs). The PPTVS is modeled considering the coexistence of external disturbances, structural parameter perturbations, and actuator failures in the system. Stability analysis is conducted for the considered PPTVS, and a sufficient condition concerning the exponential stability of the closed-loop system is given. Through a matrix polynomial approach capable of decoupling time-varying parameters, the robust fault-tolerant controller synthesis is transformed into a convex optimization problem. Flexible controller gains are enabled through selectable subinterval partitioning parameters. A sufficient condition is presented for maintaining the exponential stability, achieving
$H_{\infty}$
disturbance attenuation, and obtaining a tractable robust fault-tolerant controller. Simulation verification using a multi-input multi-output PPTVS model shows that the designed controller can maintain the exponential stability under actuator failures, satisfy the
$H_{\infty}$
performance index, and exhibiting robustness against structural parameter perturbations.