Finite-Time Robust Passive Control of Uncertain Discrete Time-Delay Systems Using Output Feedback: Application on Chua’s Circuit

Abstract

This paper investigates the finite-time robust passive control of nonlinear discrete time-delay systems via static output feedback. The considered discrete time-delay system has uncertain terms which are due to parametric uncertainties and exogenous disturbances. The disturbances are unknown time-varying signals with known upper bounds. In order to design the suitable control law, some sufficient conditions (in terms of some matrix inequalities) should be satisfied. These conditions are derived using the Lyapunov–Krasovskii functional approach. The passivity property of the closed-loop system is also presented in the form of matrix inequalities. These conditions are then converted to linear matrix inequalities (LMIs), and the gain of the controller is obtained from the feasibility testing of the resulting LMIs. Finally, the efficiency of the proposed controller is demonstrated through computer simulations for numerical and practical (Chua’s circuit) examples.