In this section
@inproceedings{Angeli:2017:10.1145/3049797.3049817,
author = {Angeli, D and Athanasopoulos, N and Jungers, RM and Philippe, M},
doi = {10.1145/3049797.3049817},
pages = {81--90},
publisher = {ACM},
title = {Path-complete graphs and common Lyapunov functions},
url = {http://dx.doi.org/10.1145/3049797.3049817},
year = {2017}
}
TY - CPAPER
AB - A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. the converse however is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding Path-Complete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path- Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another.
AU - Angeli,D
AU - Athanasopoulos,N
AU - Jungers,RM
AU - Philippe,M
DO - 10.1145/3049797.3049817
EP - 90
PB - ACM
PY - 2017///
SP - 81
TI - Path-complete graphs and common Lyapunov functions
UR - http://dx.doi.org/10.1145/3049797.3049817
UR - http://hdl.handle.net/10044/1/48521
ER -