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