Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay

This paper investigates the problem of the absolute stability of Lur'e systems with a time-varying delay. By considering the relationships among the time-varying delay, its upper bound, and the difference between them, less conservative delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov–Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results.