A new result on the global exponential stability of nonlinear neutral volterra integro-differential equation with variable lags

Abstract

In this study, the global exponential stability (GES) of the zero solution of a nonlinear neutral volterra integro-differential equation (NVIDE) with variable lags has been investigated. Based on the Lyapunov functional approach, a new stability criterion was derived for global exponential stability criterions of the considered equation. An example with numeric simulation has been given to demonstrate the applicability and accuracy of the obtained result by MATLAB Simulink.

Improved results on the stability analysis of linear neutral systems with delay decay approach

“…In Case , a Lyapunov‐Krasovskii functional can be chosen as (6) with M = L 3 = N 3 = 0. Similar to the above analysis, one can get that holds if This completes the proof.Remark In the proof of Theorems to and Corollaries 3.1 to 3.4, the interval [ t − r , t ] is divided into subintervals [ t − r , t − βr ] and [ t − βr , t ], information of delayed state x ( t − βr ) can be taken into account. It is clear that the Lyapunov function described in results of this study is more general than the ones in the literatures . Two examples are presented below to emphasize the effectiveness of the proposed method by MATLAB‐Simulink.…”

“…Therefore, the problem of stability analysis for linear systems of neutral type is a very important topic both theoretically and practically. For details, see the studies and references therein.…”

“…Neutral systems have been growing rapidly in recent years because of their successful applications in practical fields such as circuit theory, chemical engineering processes, bioengineering, nuclear reactors, population dynamics, neural networks, automatic control, and so on. When one checks the related literature, many authors focused their attention to the problem of stability via different approaches for neutral systems with linear and nonlinear uncertainties . In most studies of the stability of systems in control theory, the stability method is based on LMI and the classical Lyapunov stability theory as in the literatures .…”

“…When one checks the related literature, many authors focused their attention to the problem of stability via different approaches for neutral systems with linear and nonlinear uncertainties . In most studies of the stability of systems in control theory, the stability method is based on LMI and the classical Lyapunov stability theory as in the literatures . Furthermore, by developing a delay decay approach in delayed systems with time‐varying delays, the information of the delayed plant states can be taken into full consideration and new robust stability criteria can be obtained .…”

New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags

“…In the relevant literature, some conclusions can be reached regarding the qualitative properties of the neutral-type neural networks (see for instance, Agarwal and Grace [1], Altun and Tunç [2], El-Morshedy and Gopalsamy [5], Park [14], Park and Kwon [15], Tunç [16] and the references therein). The authors often used from several techniques such as Lyapunov-functional method, model transformations and linear matrix inequality to obtain some new necessary and sufficient conditions to ensure the stability and asymptotic stability of equation (1).…”