Exponential stability of some linear continuous time difference systems

"In this paper, we consider some classes of linear continuous time difference systems with discrete and distributed delays. For these infinite-dimensional systems, we derive new sufficient delay-dependent conditions for the exponential stability and exponential estimates for the solutions by using Lyapunov-Krasovskii functionals.

Exponential stability of linear continuous time difference systems with multiple delays

"Some recent results on exponential stability of linear continuous time difference systems with discrete and distributed delay terms are extended to the case of multiple delays. New sufficient conditions for the exponential stability and exponential estimates for the solutions by using Lyapunov–Krasovskii functionals are derived. Special attention is paid to the case of systems with commensurate discrete and distributed delays.

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.

On stability of integral delay systems

"The exponential stability of a class of integral delay systems is investigated by using the Lyapunov–Krasovskii functional approach. Sufficient delay-dependent stability conditions and exponential estimates for the solutions are derived.

Further results on exponential stability of linear continuous time difference systems

"This paper provides further Lyapunov results for the exponential stability of linear continuous time difference system involving discrete and distributed delays. We consider such a class of systems in the case when the discrete and distributed delays are independent thus completing the recent Lyapunov results obtained for the case when the delays are dependent.

A note on stability of functional difference equations

"In this note, we consider perturbed linear functional difference equations with discrete and distributed delays which play a fundamental role in several stability and stabilizability problems of time-delay systems. Linear and nonlinear perturbations are considered. Sufficient conditions for exponential stability of the perturbed solutions are given.

Exponential stability of integral delay systems with a class of analytic kernels

"The exponential stability of a class of integral delay systems with analytic kernels is investigated by using the Lyapunov-Krasovskii functional approach. Sufficient delay-dependent stability conditions and exponential estimates for the solutions are derived. Special attention is paid to the particular cases of polynomial and exponential kernels.

Stability conditions for integral delay systems

"In this paper we consider a special class of integral delay systems arising in several stability problems of time‐delay systems. For these integral systems we derive stability and robust stability conditions in terms of Lyapunov–Krasovskii functionals. More explicitly, after providing the stability conditions we compute quadratic functionals and apply them to derive exponential estimates for solutions, and robust stability conditions for perturbed integral delay systems.

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.

On computing estimates of the attraction region for a class of nonlinear time-delay systems

"In this paper, initial estimates of the attraction region for a class of nonlinear time delay systems are proposed. The approach is constructive, and make use of an appropiate Lyapunov-Krasovskii functional. Several illustrative examples (delayed logistic equation, congestion networks, hereditary phenomena in physics) complete the paper.