Canonical forms of switched linear control systems

This paper addresses the problem of finding normal forms for switched linear systems. Based on the recent controllability criterion, we decompose switched linear control systems into the controllable mode and the uncontrollable mode. For single-input controllable switched systems, we propose a canonical form via coordinate and feedback transformations. A controllable multi-input switched system can be transformed to a controllable single-input one by (nonregular) feedback reduction.