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针对连续时间线性时滞系统的负虚性判别问题,给出了若干充分性的凸优化分析结果.首先根据标准线性系统的负虚性理论给出了时滞系统的负虚性和有限频负虚性的定义.在此基础上,结合一系列的频域分析手段和不等式技术给出了可用于判断时滞系统负虚性及有限频负虚性的充分性条件,进而可通过矩阵不等式的可行解判别来实现时滞系统的负虚性以及有限频负虚性分析.算例验证了本文所得结果的有效性.
In order to solve the problem of negative definiteness of continuous time linear time-delay system, some sufficient convex optimization analysis results are given.Firstly, according to the negative virtual theory of standard linear system, On the basis of this, a sufficient condition for determining the negative and finite negative and imaginary properties of a system with time-delay is given based on a series of methods of frequency-domain analysis and inequality, which can be proved by the matrix inequalities The feasible solutions can be used to realize the negative imaginary and the finite-frequency imaginary analysis of the time-delay system.Examples demonstrate the effectiveness of the results obtained in this paper.