A Robust LMI Approach on Nonlinear Feedback Stabilization of Continuous State-Delay Systems with Lipschitzian Nonlinearities: Experimental Validation

Abstract

This paper suggests a novel nonlinear state-feedback stabilization control law using linear matrix inequalities for a class of time-delayed nonlinear dynamic systems with Lipschitz nonlinearity conditions. Based on the Lyapunov–Krasovskii stability theory, the asymptotic stabilization criterion is derived in the linear matrix inequality form and the coefficients of the nonlinear state-feedback controller are determined. Meanwhile, an appropriate criterion to find the proper feedback gain matrix F is also provided. The robustness purpose against nonlinear functions and time delays is guaranteed in this scheme. Moreover, the problem of robust H∞ performance analysis for a class of nonlinear time-delayed systems with external disturbance is studied in this paper. Simulations are presented to demonstrate the proficiency of the offered technique. For this purpose, an unstable nonlinear numerical system and a rotary inverted pendulum system have been studied in the simulation section. Moreover, an experimental study of the practical rotary inverted pendulum system is provided. These results confirm the expected satisfactory performance of the suggested method.