Algorithmic Analysis of Nonlinear Hybrid Systems

Abstract. Hybrid systems are digital real-time systems that are embedded in analog environments. Model-checking tools are available for the automatic analysis of linear hybrid automata, whose environment variables are subject to piecewise-constant polyhedral di erential inclusions. In most embedded systems, however, the environment variables have di erential inclusions that vary with the values of the variables, e.g. _x =x. Such inclusions are prohibited in the linear hybrid automaton model. We present two methods for translating nonlinear hybrid systems into linear hybrid automata. Properties of the nonlinear systems can then be inferred from the automatic analysis of the translated linear hybrid automata. The rst method, called clock translation, replaces constraints on nonlinear variables by constraints on clock variables. The clock translation is e cient but has limited applicability. The second method, called linear phase-portrait approximation, conservatively overapproximates the phase portrait of a hybrid automaton using piecewise-constant polyhedral di erential inclusions. Both methods are sound for safety properties � that is, if we establish a safety property of the translated linear system, we may conclud