  With the objective of developing computational methods for stability analysis
of switched systems, we consider the problem of finding the minimal lower
bounds on average dwell-time that guarantee global asymptotic stability of the
origin. Analytical results in the literature quantifying such lower bounds
assume existence of multiple Lyapunov functions that satisfy some inequalities.
For our purposes, we formulate an optimization problem that searches for the
optimal value of the parameters in those inequalities and includes the
computation of the associated Lyapunov functions. In its generality, the
problem is nonconvex and difficult to solve numerically, so we fix some
parameters which results in a linear program (LP). For linear vector fields
described by Hurwitz matrices, we prove that such programs are feasible and the
resulting solution provides a lower bound on the average dwell-time for
exponential stability. Through some experiments, we compare our results with
the bounds obtained from other methods in the literature and we report some
improvements in the results obtained using our method.
