On partitioned controllability of switched linear systems

When a switched linear system is not completely controllable, the controllability subspace is not enough to describe the controllability of the system over whole state space. In this case the state space can be divided into two or three control-invariant sub-manifolds, which form a control-related partition of the state space. This paper investigates when each component is a controllable sub-manifold. First, we consider when a sub-manifold is controllable for no control input case. Then the results are used to produce a necessary and sufficient condition assuring the controllability of the partitioned control-invariant sub-manifolds of a class of switched linear systems. An example is given to demonstrate the effectiveness of the results.