  This paper explores the structural controllability of switched linear
continuous-time systems. It first identifies a gap in the proof for a pivotal
criterion for the structural controllability of switched linear systems in the
literature. To address this void, we develop novel graph-theoretic concepts,
such as multi-layer dynamic graphs, generalized stems/buds, and generalized
cacti, and based on them, provide a comprehensive proof for this criterion. Our
approach also induces a new, generalized cactus based graph-theoretic criterion
for structural controllability. This not only extends Lin's cactus-based
graph-theoretic condition to switched systems for the first time, but also
provides a lower bound for the generic dimension of controllable subspaces.
