Safety and Reachability of Piecewise Linear Hybrid Dynamical Systems Based on Discrete Abstractions

In this paper, a novel methodology for analysis of piecewise linear hybrid systems based on discrete abstractions of the continuous dynamics is presented. An important characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Control specifications such as safety and reachability specifications are formulated in terms of partitions of the state space of the system. The approach provides a convenient general framework not only for analysis, but also for controller synthesis of hybrid systems. The research contributions of this paper impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems.