Recent research has shown that one can obtain a less conservative stability criterion for a continuous-time linear system with a time-varying delay by introducing a Lyapunov-Krasovskii functional with a polynomial matrix on the time-varying delay. This paper aims at analysing the stability of discrete-time linear systems with time-varying delays by introducing a delay-square-dependent Lyapunov functional. A novel convex method is presented to formulate a less conservative stability criterion, which is demonstrated through numerical simulation. Moreover, it is also shown that, if the polynomial inequality method is employed, the resultant stability criterion is inapplicable due to its extremely high numerical complexity.

最近的研究表明，通过在时变延迟上引入具有多项式矩阵的 Lyapunov-Krasovskii 泛函，可以获得具有时变延迟的连续时间线性系统的不太保守的稳定性准则。本文旨在通过引入延迟平方相关的Lyapunov 泛函来分析具有时变延迟的离散时间线性系统的稳定性。提出了一种新的凸方法来制定不太保守的稳定性准则，并通过数值模拟证明了这一点。此外，还表明，如果采用多项式不等式方法，由于其极高的数值复杂性，所得到的稳定性准则是不适用的。