Uniform asymptotic stability, an initial treatment

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered systems. It provides qualitative information about solutions, especially a characterization of the solutions' long-term trends. The asymptotic stability of a closed set, rather than of an equilibrium point, is significant since the solutions of a hybrid system often do not settle down to an equilibrium point. Furthermore, the asymptotic stability of an equilibrium point is a special case of asymptotic stability of a closed set. Namely, an equilibrium point is a closed set containing a single point.