Stability Analysis of State-Time-Dependent Nonlinear Hybrid Dynamical Systems
Stability Analysis of State-Time-Dependent Nonlinear Hybrid Dynamical Systems
复制标题
状态与时间相关的非线性混合动力系统的稳定性分析
DOI：
10.1002/tee.22807
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发表时间：
2019
影响因子：
1
通讯作者：
T. Kousaka
中科院分区：
文献类型：
--
作者：
H. Asahara;T. Kousaka
提出了一种改进的利用单值矩阵分析非线性混合动力系统稳定性的方法。我们定义了n维NHDS，并关注其初始值存在于周期轨道附近的轨道。由于系统具有非线性，电路方程不能以线性常微分方程的形式表示，这意味着现有的基于单值矩阵的稳定性分析方法不能使用，因为它需要矩阵指数。因此，我们提出了一个计算庞加莱观测中轨道摄动的一般理论。通过切换事件的扰动由状态转移矩阵表示，我们称之为跳跃矩阵。通过计算扰动，我们得到了单值矩阵，其特征乘子表示周期轨道的稳定性。我们将所提出的算法应用到具有非线性特性的中断电路中，以确认其有效性。© 2018日本电气工程师协会。由John Wiley & Sons公司出版
In this paper, we present an improved method for analyzing the stability of the nonlinear hybrid dynamical systems (NHDSs) using a monodromy matrix. We define ann‐dimensional NHDS and focus on an orbit whose initial values exist near the periodic orbit. Because the system has nonlinearity, the circuit equation cannot be expressed in the form of a linear ordinary differential equation, meaning that the existing monodromy‐matrix‐based stability analysis method cannot be used because it requires a matrix exponential. Therefore, we propose a general theory for calculating orbital perturbations during Poincaré observation. Perturbation through switching events is expressed by a state‐transition matrix, which we refer to as the saltation matrix. By computing the perturbations, we obtain the monodromy matrix, whose characteristic multipliers denote the stability of the periodic orbit. We apply the proposed algorithm to an interrupted electric circuit with a nonlinear characteristic to confirm its validity. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.