Differential and Difference Inclusions and the Filippov Theorem

The talk surveys joint works with T. Donchev and more recent ones with R. Baier.
We discuss some (continuous and discrete) versions of the celebrated Filippov
theorem on approximate solutions of differential (and difference) equations and
inclusions that  extend classical stability results for differential equations
with continuous and discontinuous right-hand sides. We present some applications
related to numerical solution of differential equations and inclusions.