A method utilizing the monodromy matrix for the derivation of the border-collision bifurcation points in switched dynamical systems

In this study, we propose a bifurcation analysis method based on the monodromy matrix that can be used to analyze border-collision bifurcation points in switched dynamical systems (SDSs). First, we present the mathematical definition of an n-dimensional SDS and the behavior of solution trajectories involving switching operations. Next, we consider perturbations of solution trajectories whose initial values lie at or near to periodic points of the system, and we describe an analysis method based on the monodromy matrix that is expanded to analyze border-collision bifurcation points. Finally, a computational implementation is presented to verify the effectiveness of the proposed method.