On the asymptotic stability for nonautonomous functional differential equations by Lyapunov functionals

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations - Preamble

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Lyapunov-razumikhin Method for Asymptotic Stability of Sets for Impulsive Functional Differential Equations

In the present paper, we study the global stability of sets of sufficiently general type with respect to impulsive functional differential equations with variable impulsive perturbations. The main results are obtained by means of piecewise continuous Lyapunov functions and the use of the Razumikhin technique.

Discussions on: "Global Output Stability for Systems Described by Retarded Functional Differential Equations: Lyapunov Characterizations

Iasson Karafyllis , Pierdomenico Pepe and Zhong-Ping Jiang Department of Environmental Engineering, Technical University of Crete, 73100, Chania, Greece; Dipartimento di Ingegneria Elettrica e dell'Informazione, Università degli Studi dell'Aquila, Monteluco di Roio, 67040, L'Aquila, Italy; Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metro...

Asymptotic stability for a class of functional differential equations

Asymptotic stability of neutral stochastic functional integro-differential equations*

This paper is concerned with the existence and asymptotic stability in the p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given in [8], and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achie...