TY - JOUR
T1 - On Path-Complete Lyapunov Functions: Geometry and Comparison
AU - Philippe, Matthew
AU - Athanasopoulos, Nikolaos
AU - Angeli, David
AU - Jungers, Raphael M.
PY - 2018/8/6
Y1 - 2018/8/6
N2 - We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another?”. Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions.
AB - We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another?”. Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions.
U2 - 10.1109/TAC.2018.2863380
DO - 10.1109/TAC.2018.2863380
M3 - Article
SN - 0018-9286
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
ER -
