
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

Stability Analysis Using Monodromy Matrix for Impacting Systems
Hiroyuki ASAHARA Takuji KOUSAKA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.6
pp.904914 Publication Date: 2018/06/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.904
Type of Manuscript: PAPER Category: Nonlinear Problems Keyword: hybrid dynamical system, impacting system, periodic border, stability analysis, bifurcation, monodromy matrix, saltation matrix,
Full Text: PDF>>
Summary:
In this research, we propose an effective stability analysis method to impacting systems with periodically moving borders (periodic borders). First, we describe an ndimensional impacting system with periodic borders. Subsequently, we present an algorithm based on a stability analysis method using the monodromy matrix for calculating stability of the waveform. This approach requires the statetransition matrix be related to the impact phenomenon, which is known as the saltation matrix. In an earlier study, the expression for the saltation matrix was derived assuming a static border (fixed border). In this research, we derive an expression for the saltation matrix for a periodic border. We confirm the performance of the proposed method, which is also applicable to systems with fixed borders, by applying it to an impacting system with a periodic border. Using this approach, we analyze the bifurcation of an impacting system with a periodic border by computing the evolution of the stable and unstable periodic waveform. We demonstrate a discontinuous change of the periodic points, which occurs when a periodic point collides with a border, in the oneparameter bifurcation diagram.

