A note on the existence of stabilizing switching signals for switched linear systems
arXiv:2011.01530
Abstract
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that are allowed to activate all subsystems. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments. We present a numerical experiment to demonstrate our results.
11 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2005.10493