A Lyapunov–Krasovskii functional with prescribed derivative whose construction does not require the stability of system is introduced. It leads to presentation stability/instability theorems. By evaluating at initial conditions depending on fundamental matrix we are able present necessary and sufficient expressed exclusively in terms delay Lyapunov for integral systems. Some examples illustrate...

This special issue on “System Theory and Delay” is dedicated to Vladimir Kharitonov the occasion of his 70th birthday, in recognition academic leadership this field research. His work systems with delays (a topic that has captured interest since early years research) reached maturity well-known contributions Lyapunov–Krasovskii functionals, delay Lyapunov matrices, prediction-based control. als...

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.