弗洛奎特理论
线性系统
LTI系统理论
非线性系统
马修函数
理论(学习稳定性)
李雅普诺夫函数
数学
数学分析
工作(物理)
转化(遗传学)
动力系统理论
控制理论(社会学)
应用数学
计算机科学
物理
化学
控制(管理)
人工智能
机器学习
基因
热力学
量子力学
生物化学
作者
Susheelkumar C. Subramanian,Sangram Redkar
出处
期刊:Journal of Computational and Nonlinear Dynamics
[ASME International]
日期:2021-01-01
卷期号:16 (1)
被引量:5
摘要
Abstract In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work, the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov–Floquet (L–F) transformation. The authors employ an intuitive state augmentation technique, modal transformation, and near identity transformations to facilitate the application of time-independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix (STM). Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.
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