  The control properties of discrete-time switched linear systems (SLS) with
switching signals generated by logical dynamic systems are studied using the
semi-tensor product (STP) approach. With the algebraic state space
representation (ASSR), the linear modes and the logical generators are
aggregated as a hybrid system, leading to the criteria of reachability,
controllability, observability, and reconstructibility of the SLSs. Algorithms
for checking these properties are given. Then, two kinds of realization
problems concerning whether the logical dynamic systems can generate the
desired switching signals are investigated, and necessary and sufficient
conditions for the realisability of the required switching signals are given
with respect to the cases of fixed operating time switching and finite
reference signal switching.
