Algorithmic Verification of Stability of Hybrid Systems
Hybrid systems refer to systems exhibiting mixed discrete-continuous behaviors and arise as a natural byproduct of the interaction of a network of embedded processors with physical systems. Hybrid systems manifest in safety critical application domains including aeronautics, automotive, robotics and power systems. Reliability is of utmost importance and a grand challenge in the area is the development of techniques and tools to aid the development of high-confidence hybrid systems.
In this talk, we focus on the verification of stability of hybrid systems. Stability is a fundamental property in control system design and captures the notion that small perturbations to the initial state or input to the system result in only small variations in the eventual behavior of the system. We present foundations for approximation based analysis of stability and concrete approximation techniques analogous to predicate abstraction for stability analysis. In contrast to the well-known methods for automated verification of stability based on Lyapunov functions, which are deductive, we present algorithmic techniques for stability analysis.