Bisimulations for Reasoning about Input-to-State Stability Properties of Hybrid Systems

In this paper, we investigate pre-orders for reasoning about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly continuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov functionions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our framework as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the