Stability Of Neutral Systems. Uncertainty Analysis

Neutral differential equations (NDEs) have the properties that are similar in some aspect to the properties of difference equations and in the other aspects are similar to the properties of differential equations. It's a complicated and difficult problem that research on the robust stability criteria for neutral systems with time-delay. In this paper, the problem of stability for neutral systems with time-delay is studied. The main purpose is to discuss the robust stability conditions for the neutral systems with mixed time-delay and uncertain time-delay ,and the Robust stability criteria for uncertain neutral systems with mixed delays and nonlinear perturbations. Some results obtained are improved and perfected. This paper mainly includes the following three parts:1. Research on the problem of the stability for uncertain neutral systems with mixed time-delay. By constructing appropriate Lyapunov functional and combining the technique of analyzing inequality, the linear matrix inequalities(LMIs) conditions for the asymptotic stability of such systems are obtained.2. Research on the problem of the robust stability for neutral systems with uncertain time-delay. By combining the Lyapunov-Krasovskii functional and LMIs method, the sufficient condition of the global asymptotic stability for the systems is derived.. The stability criteria are formulated as linear matrix inequalities (LMIs) which can be easily validated.3. Research on the problem of the delay-independent stability for the neutral systems with mixed delays and nonlinear perturbations. By combining LMIs method ,the delay-dependent robust stability criteria is obtained .Numerical examples are given to illustrate the effectiveness of the proposed method.