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Abstract: This paper outlines some preliminary work on the stability analysis of switched and hybrid systems. The hybrid systems considered are those that combine continuous dynamics, represented by differential or difference equations, with finite dynamics usually thought of as being a finite automaton. Here, we concentrate on the continuous dynamics and model the finite dynamics as switching among finitely many continuous systems. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability of such "switched systems". We use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set.>