2023/10/12 by Baier, Robert, Farkhi, Elza, Mathematisches Institut, Universität Bayreuth +1
#(strengthened) one-sided Lipschitz condition #510 #Filippov theorem #differential inclusions #monotonicity #reachable sets #set-valued Euler method
paper · doi:10.15495/epub_ubt_00007219
We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of one-sided Lipschitz maps. We prove a Filippov stability theorem for the solutions of such differential inclusions with perturbations in the right-hand side, both of the set of the velocities (outer perturbations) and of the state (inner perturbations). The obtained estimate extends the known Filippov estimate for Lipschitz maps to SOSL ones and improves the order of approximation with respect to the inner perturbation known for one-sided Lipschitz (OSL) right-hand sides from 1/2 to 1.