Estimating delay-dependent stability regions for a class of nonlinear time-delay systems

A convex approach is proposed to estimate delay-dependent stability regions for a class of nonlinear systems with a constant state-delay and subject to convex-bounded parameter uncertainty. The approach is based on a Lyapunov-Krasovskii functional with polynomial dependence on the system state and uncertain parameters. A delay-dependent stability analysis method is developed in terms of linear matrix inequalities by means of suitable system and Lyapunov function representations. Numerical examples illustrate the proposed method.