Details

Autor(en) / Beteiligte

• Philippe, Matthew
• Athanasopoulos, Nikolaos
• Angeli, David
• Jungers, Raphael M.

Titel

On Path-Complete Lyapunov Functions: Geometry and Comparison

Ist Teil von

• IEEE transactions on automatic control, 2019-05, Vol.64 (5), p.1947-1957

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2019

Link zum Volltext

• IEEE_Xplore

Quelle

IEEE Xplore

Beschreibungen/Notizen

• 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.