In this paper the global exponential stability of impulsive retarded functional differential system is investigated. By means of Lyapunov functions combined with the Razumikhin technique the effect of delay at the time of impulses for global exponential stability is obtained. This result extends some existing results in the literature. AMS subject classification: 34K20, 93D05.

The switching signal design for global exponential stability of switched neutral systems is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the global stability via the constructed switching signal. Razumikhin-like approach is used to find the stability results. Finally, some numerical examples are illustrated to show the main results.

We introduce the concept of triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are al...

ABSTRACT. This paper studies impulsive discrete systems with time delay. Several criteria on uniform stability and uniform asymptotic stability are established by utilizing the Razumikhin technique. Both linear and nonlinear impulsive discrete systems with time delay are investigated. These stability criteria show that impulses can be used to stabilize a unstable system. Some numerical examples...

This paper focuses on the problem of computing a control law which maximizes (in a sub-optimal sense) the delay of the closed-loop system for a class of linear systems with delayed input. The delay is assumed to be a continuous bounded time-varying function. The analysis is given using two diierent approaches: a Razumikhin based method and a frequency-ltering based method.

Mathematical modeling of practical situations in the field of engineering, control systems, population dynamics, disease epidemics etc. gives rise to the study of qualitative properties like stability and boundedness of solutions of many differential equations.Thisstudy aimsto establish a new stabilitycriteria forfunctionaldifferential system when the state variable depends on the previous valu...

In this paper, a new comparison principle for impulsive functional differential systems with infinite delays or finite delays is investigated. Also, some sufficient conditions for exponential stability are presented by using Lyapunov functions and Razumikhin technique. The results improve and generalize the ones in the literature. Finally, an example is given to illustrate the feasibility and a...

Without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections, we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the Cohen–Grossberg neural network with multiple delays. Lyapunov functionals and functions combined with the Razumikhin technique are employed. The criteria are all indepen...