Title: On reduction of differential inclusions and Lyapunov stability,
Abstract: In this paper, locally Lipschitz regular functions are utilized to identify
and remove infeasible directions from differential inclusions. The resulting
reduced differential inclusion is point-wise smaller (in the sense of set
containment) than the original differential inclusion. The reduced inclusion is
utilized to develop a generalized notion of a derivative in the direction(s) of
a set-valued map for locally Lipschitz candidate Lyapunov functions. The
developed generalized derivative yields less conservative statements of
Lyapunov stability results, invariance-like results, and Matrosov results for
differential inclusions. Illustrative examples are included to demonstrate the
utility of the developed stability theorems.