Comparison of path-complete Lyapunov functions via template-dependent lifts

This paper investigates, in the context of discrete-time switched systems, problem comparison for path-complete stability certificates. We introduce and study abstract operations on graphs, called lifts, which allow us to recover previous results a general framework. Moreover, this approach highlights existing relations between analytical properties chosen set candidate Lyapunov functions (the template) admissibility certain lifts. provides new methodology characterization ordering relation criteria, when particular template is chosen. apply our specific templates, notably sets primal dual copositive norms, providing certificates positive systems. These tools are finally illustrated with aim numerical examples.