A Comparison Theory for the Stability Analysis of General Hybrid Systems

摘要

In some of our recent work, a general model for hybrid dynamical systems was proposed whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time. By transforming this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties, but defined on real time, we established the Principal Lyapunov Stability Results as well as Lagrange Stability Results. Making use of stability preserving mappings, results which comprise a general comparison theory for hybrid dynamical systems can be developed and these results can be specialized by employing vector Lyapunov functions. It then can be shown that the latter results can be used to yield the Principal Lyapunov Stability Results discussed above as special cases. Due to space limitations, only a summary of the paper is presented.