Differential inclusions with stable subinclusions

wherexER”,tE[tO,T]andF:R”x[tO,T] G. R" is a set-valued mapping with compact and convex images. An absolutely continuous function x(m) is a solution of (1) if it satisfies (1) for a.e. t E [to, T]. Thus, a differential inclusion generalizes an ordinary differential equation by permitting a set-valued right-hand side. Differential equations containing either control/ uncertain parameters or discontinuity in the right-hand side can be transformed into the framework of (1) [l, 21. A well-known and very useful result due to Filippov [3] estimates the uniform distance from an arbitrary absolutely continuous function x( -) to the set of solutions of (1) starting from x(t,) by means of constant times the “deviation”