李雅普诺夫定理在多速率系统数值稳定性研究中的应用

Luc-André Grégoire, Mohammad Sleiman, Handy Fortin-Blanchette, K. Al-haddad
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引用次数: 3

摘要

提出了一种分析多速率系统稳定性的方法。多速率系统采用不同的采样率来模拟电路的不同部分。这可以减少刚性系统的计算负担;根据所研究现象的时间常数选择最合适的时间步长。传统上,离散系统的稳定性是通过研究系统的特征值来确定的,这种方法只能使用单一的采样时间,因此不能应用于多速率系统。在文献中可以找到许多以多速率进行模拟的例子,除了模拟结果外,没有其他稳定性证明。本文首先用单时间步长将多速率系统表示为非线性系统,然后用李雅普诺夫定理证明了多速率系统的稳定性。数值算例验证了该方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical stability of multi-rate system using Lyapunov's theorem: Applied to real-time simulation
This paper proposes a method to analyse stability of multi-rate system. Multi-rate systems are used to simulate different part of the circuit with different sampling rate. This allows to reduce computational burden of stiff system; by choosing the most appropriate time-step according to the time constant of the phenomena studied. Traditionally, stability of discrete system is done by studying the eigenvalues of the system which can only uses a single sampling time and therefore cannot be applied to multi-rate systems. Many examples, where simulation is done with multiple rate, can be found in literature with no proof of stability other than simulation results. In this paper, multi-rate system are first represented as non-linear system using a single time-step and their stability is then demonstrated using Lyapunov's theorem. The proposed method is supported by a numerical example.
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