Finite-time resilient control for uncertain periodic piecewise polynomial time-varying systems

Abstract

This study explores the problem of finite-time resilient control for periodic piecewise polynomial time-varying systems in the face of parameter uncertainties, time-varying state delays and external disturbances. Particularly, the considered system is characterized by dividing the fundamental period of periodic systems into numerous subintervals, each of which can be expressed by using matrix polynomial functions. The foremost intention of this work is to lay out a resilient controller such that the resulting closed-loop system is finite-time bounded and satisfies a mixed $H_{\infty }$ and passivity performance index. Furthermore, by constructing a periodic piecewise time-varying Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in line with Wiritinger’s inequality and matrix polynomial lemma to guarantee the needed outcomes of the system under study. Following this, the gain matrix of the devised controller can be calculated by solving the established constraints. As a final step, we conclude with a numerical example that validates the potential and importance of the theoretical discoveries and the developed control scheme.