Daniel Melchor-Aguilar

On delay-dependent stability conditions ☆

It is quite common in stability analysis of time-delay systems to make a special transformation of the system under investigation in order to obtain stability conditions which depend on the values of the delays. In this note we discuss additional conditions for stability and robust stability of the transformed system which do not appear when the original system is considered.

On delay-dependent stability conditions for time-varying systems

In this paper, some recent results on additional dynamics for transformed time-delay systems are extended to the case of time-varying systems. Special equations which describe these dynamics are derived. Additional restrictions on stability and robust stability imposed by the transformations are obtained.

Estimates of the attraction region for a class of nonlinear time-delay systems

In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form ẋ=Ax(t) + (t - h (t) + f (x(t), x (t-h (t))) The approach is constructive and makes use of a Lyapunov-Krasovskii functional associated to the linear part. Several illustrative examples (delayed logistic equation, stabilizing nonlinear oscillations by delayed output feedback, congestion control in high-performance networks and hereditary phenomena in physics) complete the presentation. The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.

On stability of integral delay systems

Abstract 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.

Additional dynamics for general class of time-delay systems

In this note, some recent results on additional dynamics introduced by transformations of time-delay systems are extended to the case of general time-varying systems with delay. Sufficient stability conditions for the additional dynamics are also 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.

Exponential stability of some linear continuous time difference systems

Abstract 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

Abstract 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.

Computing non-fragile PI controllers for delay models of TCP/AQM networks

This article focuses on the stabilisation problem of fluid-flow delay models of transmission control protocol/active queue management (TCP/AQM) networks by using a proportional-integral (PI) controller as AQM strategy. More precisely, the complete set of PI controllers that exponentially stabilises the corresponding linear time-delay system is derived. Using the particular geometric properties of this set of the controller parameters, the issues of robustness to uncertainty in the network parameters and to perturbation in the controller coefficients are addressed. Then, a methodology to compute a non-fragile PI AQM controller is provided. Finally, exponential estimates for the closed-loop system solutions, allowing to evaluate the performance of the corresponding PI-controlled closed-loop system, are proposed by using a Lyapunov–Krasovskii functional approach. An illustrative example completes the presentation.

Further results on exponential stability of linear continuous time difference systems

Abstract 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.