  Linear constrained switching systems are linear switched systems whose
switching sequences are constrained by a deterministic finite automaton. This
work investigates how to generate a sequence of matrices with an asymptotic
growth rate close to the constrained joint spectral radius (CJSR) for
constrained switching systems, based on our previous result that reveals the
equivalence of a constrained switching system and a lifted arbitrary switching
system. By using the dual solution of a sum-of-squares optimization program, an
algorithm is designed for the lifted arbitrary switching system to produce a
sequence of matrices with an asymptotic growth rate that is close to the CJSR
of the original constrained switching system. It is also shown that a type of
existing algorithms designed for arbitrary switching systems can be applied to
the lifted system such that the desired sequence of matrices can be generated
for the constrained switching system. Several numerical examples are provided
to illustrate the better performance of the proposed algorithms compared with
existing ones.
