Stability Of Neutral Functional Differential Equations

Neutral differential equations (NDEs) have the properties that are similar in someaspect to the properties of difference equations and in the other aspects are similar to theproperties of differential equations. This duality of NDE is essential for a study ofasymptotic behavior of their solutions. In this paper, the problem of stability for neutralsystems with time-delay is studied, and the main purpose is to discuss the robuststability conditions for the neutral systems with distributed delay and the robustabsolute stability conditions for the Lurie systems. Some results obtained are improvedand perfected. This paper mainly includes the following four parts:1. Research on the problem of the stability for neutral systems with distributed delay.By constructing appropriate Lyapunov functional and combining the technique ofanalyzing inequality, the linear matrix inequalities(LMIs) which are discrete-delay-independent and neutral-delay-independent while distributed-delay-dependent c-onditions for the asymptotic stability of such systems are obtained. Numericalexamples are given to illustrate the effectiveness of the proposed method.2. More research on the problem of the stability for neutral systems with distributeddelay. Firstly, we construct the Lyapunov functional, and then add some appropriatezero terms to the deviation of the Lyapunov functional and construct some linearmatrix inequalities. Then the delay-dependent asymptotic stability and robuststability sufficient conditions is derived. Finally, numerical examples are given todemonstrate the derived condition is less conservative than that given in someexisting literatures.3. Research on the problem of the delay-independent absolute stability for the neutalLurie control systems. By constructing appropriate Lyapunov functional andcombining the technique of analyzing inequality, delay-independent linear matrixinequalities conditions for the absolute stability of such systems are obtained.4. Research on the problem of the delay-independent absolute stability for the Luriecontrol systems. Based on the character of the system itself, we construct the rightLyapunov functional and make use of some useful inequality, and then the linear in- equality conditions for the delay-independent absolute stability of the Lurie controlsystems are obtained.