论文标题
关于由Legendre近似产生的时间延迟系统足够的LMI条件
On the necessity of sufficient LMI conditions for time-delay systems arising from Legendre approximation
论文作者
论文摘要
这项工作用于使用Lyapunov-Krasovskii定理的时间延迟系统的稳定性分析。这种方法已被广泛用于文献中，已经提出了许多足够的稳定条件，并表示为线性基质不等式（LMI）。对通常指出的方法的主要批评是这些LMI条件仅足够，并且缺乏有关减少保守主义的信息。最近，已经使用Bessel-Legendre不等式或基于多项式的不等式研究了可扩展方法。这些方法的兴趣取决于其分层结构，并保证降低保守主义水平。但是，融合仍然是一个悬而未决的问题，本文将首次回答。目的是证明时间延迟系统的稳定性意味着这些可扩展的LMI的可行性，在足够大的Legendre多项式中。此外，拟议的贡献甚至能够对此顺序进行分析估计，从而为时间延迟系统的稳定性提供了必要和足够的LMI。
This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov-Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability have been proposed and expressed as linear matrix inequalities (LMI). The main criticism of the method that is often pointed out is that these LMI conditions are only sufficient, and there is a lack of information regarding the reduction of the conservatism. Recently, scalable methods have been investigated using Bessel-Legendre inequality or orthogonal polynomial-based inequalities. The interest of these methods relies on their hierarchical structure with a guarantee of reduction of the level of conservatism. However, the convergence is still an open question that will be answered for the first time in this paper. The objective is to prove that the stability of a time-delay system implies the feasibility of these scalable LMI, at a sufficiently large order of the Legendre polynomials. Moreover, the proposed contribution is even able to provide an analytic estimation of this order, giving rise to a necessary and sufficient LMI for the stability of time-delay systems.
