# Pre-orders for Reasoning about Input-to-State Stability Properties of Hybrid Systems

### Pavithra Prabhakar, Jun Liu and Richard M. Murray

Submitted, Hybrid Systems: Computation and Control (HSCC) 2013

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 con- tinuous 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 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 original system.

- Conference Paper: http://www.cds.caltech.edu/~murray/preprints/plm13-hscc_s.pdf
- Project(s): Template:HTDB funding::UTRC, Boeing