We consider a class of  nonautonomous  systems  differential  equations with time-varying concentrated and distributed  delays  than  can be unbounded.  Using Lyapunov–Krasovskii functional, some estimates of solutions are established. The obtained allow us to conclude whether the stable.

This work addresses the problems of robust exponential stability and stabilization for uncertain linear non-autonomous control systems with discrete and distributed time-varying delays and nonlinear perturbations. Based on the combination of the Riccati differential equation approach and the Lyapunov-Krasovskii functional, new sufficient conditions are derived in terms of the solution of Riccat...

Abstract—In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness ...

Converse Lyapunov–Krasovskii theorems for systems described by neutral functional differential equations in Hale's form Pierdomenico Pepe a & Iasson Karafyllis b a Department of Information Engineering, Computer Science, and Mathematics, University of L'Aquila, 67100 L'Aquila, Italy b Department of Environmental Engineering, Technical University of Crete, Chania 73100, Greece Version of record ...

Wemake the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and ...

A mathematical driver model is given in the spacial equation form, which takes into account the previewed information of the path. Optimal control method is considered for the ideal no time-delay case and Lyapunov-Krasovskii functional approach is applied to deal with drivers’ reaction time-delay. For both cases, exponential stability is guaranteed for the closedloop system.

This paper studies the problem of robust exponential stability of uncertain perturbed neutral system with time varying delay. By introducing a novel Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs. Numerical examples are given to illustrate the theoretical developments.

Systems with delays are a specific group of dynamic systems. The fact that some delays can be short and some can be long makes system analysis and control design much more complex. In this paper we present a proposal to solve the problem of stability and control design of continuous time systems with time-varying delays. Based on the Lyapunov-Krasovskii functional the stability condition is der...

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite-dimensional linear dynamical system and an infinite-dimensional time delay operator, we show that...

We investigate the exponential stability of a linear system neutral-type with variable time lags. By using Newton–Leibniz formula and Lyapunov–Krasovskii functional, we prove two results on solutions. The criteria are stated in form matrix inequalities. MATLAB-Simulink software, present numerical examples illustrating applicability our assumptions. obtained extend generalize already known avail...