Teaching time-varying stability theory using autonomous partial stability theory

摘要

We present partial stability results; that is, stability with respect to part of the system's state, for nonlinear dynamical systems. Using these results we provide a rigorous unification between partial stability theory for autonomous systems and stability theory for nonlinear time-varying systems. This unification allows for time-varying stability theory to be presented as a special case of autonomous partial stability theory in a first course on nonlinear systems.