We present a technique for analysis of asymptotic stability for a
class of differential inclusions. This technique is based on the
Lyapunov-type theorems. The construction of the Lyapunov functions
for differential inclusions is reduced to an auxiliary problem of mathematical
programming, namely, to the problem of searching saddle points of
a suitable function. The computational approach to the auxiliary
problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems
described by difference inclusions. The obtained numerical schemes
are applied to some illustrative examples