Robustness of homogeneous and locally homogeneous differential inclusions

The paper proposes constructive conditions for verification of input-to-state stability property for discontinuous systems using geometric homogeneity. Two sets of conditions are developed: for a class of homogeneous and locally homogeneous systems described by differential inclusions. The advantage of the proposed conditions is that they are not based on the Lyapunov function method, but more related to algebraic operations over the right-hand side of the system.