On an extension of homogeneity notion for differential inclusions

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. Theorem of L. Rosier [1] on a homogeneous Lyapunov function existence for homogeneous differential inclusions is presented. An extension of the result of Bhat and Bernstein [2] about the global asymptotic stability of a system admitting a strictly positively invariant compact set is also proved.