广义时滞系统的稳定性条件  

Stability Condition of Singular Time-delay Systems

作　　者：于姗姗 YU Shanshan(School of Mathematics and System Science,Shenyang Normal University,Shenyang,Liaoning 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《平顶山学院学报》2020年第2期19-24,共6页Journal of Pingdingshan University

摘　　要：研究了广义时滞系统的稳定性问题.首先,将广义时滞系统转化为等价的中立时滞系统模型.然后,通过将二次型中的向量增加维数构造了增广的Lyapunov-Krasovskii泛函(简称L-K泛函),使用四阶Bessel-Legendre积分不等式(简称B-L积分不等式)处理L-K泛函导数的一重积分项,得到了一个新的保守性更小的稳定性充分条件,并以线性矩阵不等式(简称LMI)的形式给出.最后,通过两个数值算例说明了所提方法比现有方法具有更小的保守性.The stability condition of singular time-delay systems is addressed. Firstly,the singular time-delay systems are transformed into equivalent neutral time-delay systems. Secondly,an augmented Lyapunov-Krasovskii functional( L-K functional) is constructed by augmented dimension of vector in the quadratic form. Derivation on the L-K function produces single integral term which is dealt with fourth-order integral Bessel-Legendre inequality( B-L inequality). Then,the stability condition of singular time-delay systems is obtained in the form of linear matrix inequality( LMI). Finally,two numerical examples are illustrated to show that the proposed method is less conservative than other existing ones.

关 键 词：广义时滞系统 中立时滞系统 稳定性 Lyapunov-Krasovskii泛函(L-K泛函) Bessel-Legendre积分不等式(B-L积分不等式) 

分 类 号：O231[理学—运筹学与控制论]