Interpretability of Path-Complete Techniques and Memory-Based Lyapunov Functions

We study path-complete Lyapunov functions, which are stability criteria for switched systems, described by a combinatorial component (namely, an automaton), and functional (a set of candidate called the template). introduce class based on what we call memory-based generalize several techniques in literature. Our main result is equivalence result: any function equivalent to function, however defined another template. show usefulness our terms numerical efficiency via academic example.