Stability and Euler Approximation of One-sided Lipschitz Differential Inclusions

Abstract

Ordinary differential and functional-differential inclusions with compact right-hand sides are considered. Stability theorems of Filippov's type in the convex and nonconvex case are proved under a one-sided Lipschitz condition, which extends the notions of Lipschitz continuity, dissipativity, and the uniform one-sided Lipschitz condition for set-valued mappings. The accuracy of approximation of the solution sets by means of the Euler discretization scheme for both types of inclusions is estimated.