Modeling and Verification of Sampled-Data Hybrid Systems

We introduce sampled data hybrid automata (SDHA) as a formal model of hybrid systems that result from clock-driven computer control of continuous dynamic sytems. In contrast to standard hybrid automata, the discrete state transitions in the SDHA can occur only at valid sampling times when the guard conditions are evaluated. Sequences of valid sampling times are defined by a clock structure that specifies bounds on the possible initial phases, period variations and jitter. Approximate quotient transition systems are then defined for SDHA as a theoretical framework for performing formal verification. The concepts introduced in this paper are illustrated by a numerical example. The paper concludes with a discussion of current research aimed at developing a tool for verifying prorperties of real sampled data control systems.