I am taking a nonlinear control class. As we were discussing stability, we came across 'weaker' and 'stronger' stability conditions. For example asymptotic stability (AS) is stronger than stability in the sense of lyapunov (SISL), and exponential stability (ES) is stronger than AS. Then we across local and global definitions of stability.
The question then arises, if for some system we have a global form of some stability, say AS, and a local form of another 'stronger' stability for the same system, say ES, then which statement is actually stronger. Or does it so happen that global AS + local ES => global ES?