An augmented approach to absolute stability for uncertain Lur'e system with time‐varying delay

Abstract

This paper investigates the absolute stability criteria of Lur'e system with time‐varying delays, uncertainties, and sector bounded nonlinearities. By constructing suitable Lyapunov–Krasovskii functionals (LKFs) and utilizing some useful mathematical techniques, an improved delay‐dependent stability criterion is introduced in Theorem 1. Based on the result of Theorem 1, a further enhanced criterion is proposed in Theorem 2 by employing the augmented zero equality approach. Finally, two numerical examples show the improved performance of the criteria by comparing maximum delay bounds.

General stability criteria for time‐delay systems using a new delay‐dependent reciprocally convex inequality

“…However, the integrals of a quadratic term appeared in the derivative of LKFs would produce reciprocal convex combination terms [23, 24], for example, $$$ \frac{1}{\alpha }{\beta}_1^TR{\beta}_1+\frac{1}{1-\alpha }{\beta}_2^TR{\beta}_2 $$$, which are a challenging problem. To handle the reciprocal convex combination term, a reciprocally convex inequality (RCI) is a crucial and several versions of the RCIs have been reported in recent years.…”