线性时滞系统的时滞相关稳定性新判据

来源期刊：中南大学学报(自然科学版)2004年第3期

论文作者：张先明 吴敏 何勇

文章页码：438 - 442

关键词：线性系统;时滞相关;渐近稳定;线性矩阵不等式

Key words：linear systems; delay-dependent; asymptotic stability; linear matrix inequality

摘    要：提出一种新的积分不等式方法,讨论线性时滞系统的时滞相关稳定性。首先利用Leibniz-Newton公式以及ark不等式,建立一系列基于二次型项的积分不等式,然后利用这些不等式以及Lyapunov-Krasovskii泛函方法,获得一系列基于LMI的时滞相关稳定条件。实践结果表明,利用积分不等式方法所得的时滞稳定界限具有较小的保守性。

Abstract: This paper proposes a new method-integral inequality approach to discusses the condition of delay dependent which can guarantees the stability of systems with state delay. First, a series of integral inequalities based on quadratic term are formulated by combining Leibniz-Newton formula with Park inequality. Next, using Lyapunov-Krasovskii functional method, the sufficient conditions of delay-dependent stability based on linear matrix inequality are derived to ensure that linear system with state delay is asymptotically stable, which take the existing results as special cases. Last, some examples are given to illustrate that the new method is more effective than the present methods and the delay bounds obtained in this paper are of less conservative.