离散线性多时滞系统稳定的充分必要条件
A Sufficient and Necessary Condition for Discrete LTI System with Multi-Delays
DOI: 10.12677/DSC.2021.102013, PDF,   
作者: 张志飞, 陈丹凤：佛山科学技术学院机电与自动化学院，广东 佛山；年晓红：中南大学信息科学与电气工程学院控制系，湖南 长沙
关键词: 线性时滞系统；Lyapunov矩阵不等式；二次型；谱半径；强稳定性；
摘要: 时滞线性离散系统的稳定性研究，当N > 2时是一个具有挑战性的难题。本文使用离散Lyapunov矩阵不等式结合复域空间二次型函数，利用二次型符号及连续函数的特性将稳定性计问题转换成多变量的极值问题，获得了时滞线性离散系统强稳定的充分必要条件，且表达形式较现有成果更简洁，具有较低的计算复杂度，较之现有计算复杂度n2，论文只需在n规模上进行。文末借助经典实例，通过与现有方法的对比，进一步论证了本文结论的可行性和有效性。
Abstract: The stability of linear discrete system is a challenge. By combing the discrete Lyapunov matrix inequality with the time-domain spatial quadratic function, a novel sufficient and necessary condition for strong stability which is more concise than the existing results is obtained. It transfers the problem of spectral radius into that of judging sign of a quadric form by using the properties of continuous function with multi-variables. Finally, the feasibility and effectiveness of the proposed method are further verified by comparing with the existing methods with the classical examples.
文章引用：张志飞, 陈丹凤, 年晓红. 离散线性多时滞系统稳定的充分必要条件[J]. 动力系统与控制, 2021, 10(2): 120-128. https://doi.org/10.12677/DSC.2021.102013

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