  In this paper, we consider the perturbation analysis for the periodic
generalized coupled Sylvester (PGCS) equation. The normwise backward error for
this equation is first obtained. Then, we present its normwise and
componentwise perturbation bounds, from which the normwise and effective
condition numbers are derived. Moreover, the mixed and componentwise condition
numbers for the PGCS equation are also given. To estimate these condition
numbers with high reliability, the probabilistic spectral norm estimator and
the statistical condition estimation method are applied. The obtained results
are illustrated by numerical examples.
