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We propose a novel framework for the Lyapunov analysis of a large class ofhybrid systems, inspired by the theory of symbolic dynamics and earlier resultson the restricted class of switched systems. This new framework allows us toleverage language theory tools in order to provide a universal characterizationof Lyapunov stability for this class of systems. We establish, in particular, aformal connection between multiple Lyapunov functions and techniques based onmemorization and/or prediction of the discrete part of the state. This allowsus to provide an equivalent (single) Lyapunov function, for any givenmultiple-Lyapunov criterion. By leveraging our Language-theoretic formalism, anew class of stability conditions is then obtained when considering both memoryand future values of the state in a joint fashion, providing new numericalschemes that outperform existing technique. Our techniques are then illustratedon numerical examples.

Multiple Lyapunov Functions and Memory: A Symbolic Dynamics Approach to Systems and Control