  This paper studies the constrained switching (linear) system which is a
discrete-time switched linear system whose switching sequences are constrained
by a deterministic finite automaton. The stability of a constrained switching
system is characterized by its constrained joint spectral radius that is known
to be difficult to compute or approximate. Using the semi-tensor product of
matrices, the matrix-form expression of a constrained switching system is shown
to be equivalent to that of a lifted arbitrary switching system. Then the
constrained joint/generalized spectral radius of a constrained switching system
is proved to be equal to the joint/generalized spectral radius of its lifted
arbitrary switching system which can be approximated by off-the-shelf
algorithms.
