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A technique is presented 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. The main result is also extended to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples. It is conceivable that one can use the proposed computational approach and the corresponding results of the so called receding horizon control. Moreover, this approach can also be applied to some other classes of continuous and discrete control systems governed by differential and difference inclusions.