Delay-Dependent Regional Stability of a Class of Uncertain Nonlinear State-Delayed Systems

This paper proposes a convex approach to regional stability analysis of a class of nonlinear state-delayed systems subject to convex-bounded parameter uncertainty. Delay-dependent conditions are developed to ensure the system robust local stability and obtain an estimate of a domain of attraction of the origin inside a given polytopic region of the state-space. The proposed approach is based on a Lyapunov-Krasovskii functional with polynomial dependence on the system state and uncertain parameters and is formulated in terms of linear matrix inequalities. Numerical examples illustrate the potentials of the derived results.