2021 年 12 巻 3 号 p. 237-256
This study reports a stability analysis method based on the monodromy matrix for switched dynamical systems. First, we focus on nonlinear autonomous interrupted systems. In the electrical field, for example, most circuit equations are described in the form of a linear ordinary differential equation. However, with the growth of clean energy power generation devices, the nonlinear term appears in the circuit equation as represented by the photovoltaic module. From this point of view, we discuss a stability analysis method based on the monodromy matrix for nonlinear interrupted systems. Second, we consider impacting systems with a periodic threshold. The previous stability analysis method based on the monodromy matrix is only applicable to impacting systems with fixed threshold. We improved this method considering the periodic threshold. Many impacting systems in the engineering field have a periodic threshold; hence, we introduce this method herein with a mechanical application example. We aim to contribute to the development of the nonlinear theory using above-mentioned two topics.
