Stability Preserving Simulations and Bisimulations for Hybrid Systems


Pre-orders and equivalence relations between processes, like simulation and bisimulation, have played a central role in the minimization and abstraction primarily based verification and analysis of discrete-state systems for modal and temporal properties. During this paper, we investigate the pre-orders and equivalence relations on hybrid systems that preserve stability. We initial show that stability with respect to reference trajectories isn't preserved by either the traditional notion of bisimulation or the additional recently proposed stronger notions with additional continuity constraints. We introduce the concept of uniformly continuous simulation and bisimulation—specifically, simulation and bisimulation with some extra uniform continuity conditions on the relation—which will be used to reason concerning stability of trajectories. Finally, we have a tendency to show that uniformly continuous simulations and bisimulations are widely prevalent, by recasting many classical results on proving stability of dynamical and hybrid systems as establishing the existence of a straightforward, obviously stable system that (bi)-simulates the given system through uniformly continuous (bi)-simulations. We tend to conjointly discuss briefly a replacement abstraction technique for stability analysis which is based on the foundations developed in the paper.

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