Delay-Dependent Robust Stability Analysis for Uncertain Nonlinear Systems

Abstract

As a popular topic, robust stability for uncertain systems with time delay have been widely studied in various engineering, biological, economical, electronic and dynamical systems, nerve network and so on. Recently, many researchers have paid a lot of attentions on the problem of robust stability for uncertain nonlinear systems with time delay. In this paper, a type of uncertain nonlinear delay systems has been considered in robust stability analysis. A novel robust stability criterion of the system is derived by using Lyapunov method and quadratic stability theory. A new upper bound with high-level infinite small on time delay based on Hariwity matrix and a solvable algebraic Riccati equation is presented. The main results are as follows: Through Lyapunov function and a solvable algebraic Riccati equation, we obtain the criterion of robust stability (exponential stability) for uncertain nonlinear systems with time delay.