含有混合时滞的不确定中立系统的稳定性条件  

Stability Criteria in Uncertain Neutral Systems with Mixed Time-Varying Delays

作　　者：王月娥[1] 吴保卫[1] 陈佳[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《重庆师范大学学报（自然科学版）》2010年第3期52-57,90,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10571114);陕西省自然科学基础研究计划项目(No.SJ08A20)

摘　　要：本文研究了一类带有时变时滞的非线性中立系统时滞依赖的稳定性条件,系统模型为:(t)-C(t-h(t))=Ax(t)+Bx(t-(t))+F(x(t),t)+G(x(t-(t)),t)。在本文中,时变时滞假定属于一个区间m≤(t)≤M。目的是对于所容许的不确定性和时滞得到一个新的具有更低保守性的能够使系统达到渐近稳定的充分条件。在本文中有效地利用了时变时滞的变化区间的上下界这一信息,并且利用了牛顿-莱布尼茨公式,构造了新的Lyapunov泛函,基于S-Procedure引理得到了新的判别带有非线性不确定性中立系统渐近稳定的充分条件:∑<0。最后通过数值算例来验证了此方法的可行性以及更低的保守性。This paper investigates the stability condition in a class of uncertain neutral systems with interval time-varying delays and nonlinear uncertainties. In this paper, the time-varying delays are assumed to belong to an interval ：τm ≤ τ（t） ≤τM. The purpose is to derive a new delay-dependent stability condition with much less conservative in the neutral system, irrespective of the uncertainties and the time delays. Based on both the lower and upper bounds of time-varying delay interval, in the choice of the approriate Lyapunov function, used the transform of Leibnitz-Newton formula, a new delay-dependent stability condition of nonlinear neutral systems with time-varying delays is derived which is based on S-prosedure ：∑ 〈 0. Finally, numerical examples show the effectiveness of our results and much less conservative.

关 键 词：中立系统 渐近稳定性 时变时滞 非线性 线性矩阵不等式(LMI) 

分 类 号：O231[理学—运筹学与控制论]