Continuous-time switched systems with switching frequency constraints: Path-complete stability criteria

We propose a novel Lyapunov construction for continuous-time switched systems relying on graph theoretical construction. Starting with finite family of continuously differentiable functions, suitable inequalities involving these functions and the vector fields defining system are encoded in direct labeled graph. then provide sufficient conditions (asymptotic) stability subject to constrained switching times, by path-completeness chosen The analysis is first carried out under hypothesis constant frequency. Then, results generalized dwell time setting. In case linear dynamics, formalism allows us interpret existing unified language. Some numerical examples illustrate usefulness conditions.