Finite-Time Stabilization of Descriptor Time-Delay Systems with One-Sided Lipschitz Nonlinearities: Application to Partial Element Equivalent Circuit

This paper deals with the design of a stabilizing state feedback controller for a class of nonlinear time-delay descriptor system over the finite-time interval. The considered system is exposed to parameter uncertainties and time-varying disturbances. To provide a wider and more general class of nonlinear time-delay descriptor systems, the nonlinear parts of the system are assumed to be a function of state variables, delayed state variables, input and also delayed input and to satisfy the one-sided Lipschitz condition. The purpose of finite-time control is to propose a robust control law such that the resulting closed-loop system is stable, impulse free and regular for all admissible model uncertainties over the considered time interval. Additionally, the designed controller ensures the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H_{\infty } $$\end{document} disturbance attenuation of the closed-loop descriptor system. In order to achieve these goals, two theorems are given. The sufficient conditions are gained based on the delay-dependent analyses. These conditions then are converted to solvable linear matrix inequalities (LMIs). Finally, simulations are provided a practical example, to confirm the theoretical achievements. The practical example is a partial element equivalent circuit which is a neutral time-delay system. This system is transformed into a time-delay descriptor system. Simulation outcomes illustrate the effective performance of the given method in robust finite-time stabilization.