Finite time Controller Design for Time-Delay One-sided Lipschitz Systems

This article studies dynamical systems with one-sided Lipchitz nonlinear functions in the presence of time-delay and unknown terms due to model uncertainties and external disturbances. The one-sided Lipchitz condition is less conservatism with respect to well-known Lipchitz condition and includes a wider class of nonlinear functions. The goal of this paper is design of state feedback controller for the considered system which guarantees the robust and finite time stability of the state variables of the closed-loop system. For this purpose, based on the Lyapunov approach in stability analysis of time-delay systems; the appropriate Lyapunov-Krasovskii functional is selected and the sufficient conditions for robust finite-time stabilization are given based on linear matrix inequalities. The feedback gain is also calculated by solving the obtained matrix inequalities. Finally, numerical examples and simulations are given to show the performance of the proposed method. Additionally, it is shown that the proposed theorem has been less conservative and its functional range is wider.