Delay-dependent robust stability and ℒ2ℒ2-gain analysis of a class of nonlinear time-delay systems

A convex approach to robust regional stability analysis of a class of nonlinear state-delayed systems subject to convex-bounded parameter uncertainty is proposed. Delay-dependent conditions are developed to ensure 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. This approach is then extended to provide a delay-dependent solution to the problem of ℒ2ℒ2-gain analysis. 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.