Lyapunov Theorems for Systems Described by Retarded Functional Differential Equations

Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided

Robust stability of integral delay systems with exponential kernels

"In this chapter the stability analysis via Lyapunov-Krasovskii method is extended to perturbed integral delay systems with exponential kernels. Several sufficient robust stability conditions given in the form of linear matrix inequalities are derived.

New results on robust exponential stability of integral delay systems

"The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov–Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.