线性时滞系统的时滞相关稳定性新判据

New criteria on delay-dependent stability for linear systems with delay

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Park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。

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.