Stability boundary analysis of nonlinear dynamics subject to state limits

In the spirit of Morse-Smale systems, the paper analyzes the structure of stability boundary of a stable equilibrium point for nonlinear dynamics subject to state limits. Presence of state limits implies that the underlying dynamics does not satisfy the Lipschitz condition for solution existence/uniqueness. There does not exist a smooth flow for the dynamics thus complicating traditional analysis of stability boundary. By analyzing geometric properties of the solutions of the constrained dynamics, the paper establishes a characterization of the stability boundary under rather strong assumptions as a first step towards detailed boundary characterization.