Robust stability of nonlinear time‐delay systems with interval time‐varying delay

This paper deals with the problem of obtaining delay‐dependent stability conditions and L₂‐gain analysis for a class of nonlinear time‐delay systems with norm‐bounded and possibly time‐varying uncertainties. No restrictions on the derivative of the time‐varying delay are imposed, though lower and upper bounds of the delay interval are assumed to be known. A Lyapunov–Krasovskii functional approach is proposed to derive novel delay‐dependent stability conditions which are expressed in terms of linear matrix inequalities (LMIs). To reduce conservatism, the work exploits the idea of splitting the delay interval in multiple regions, so that specific conditions can be imposed to a unique functional in the different regions. This improves the computed bounds for certain delay‐dependent integral terms, providing less conservative LMI conditions. Examples are provided to demonstrate the reduced conservatism with respect to the available results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.