Philippe, Matthew
[UCL]
Athanasopoulos, Nikolaos
[UCL]
David, Angeli
Jungers, Raphaël M.
[UCL]
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
Bibliographic reference |
Philippe, Matthew ; Athanasopoulos, Nikolaos ; David, Angeli ; Jungers, Raphaël M.. On Path-Complete Lyapunov Functions: Geometry and Comparison. In: IEEE Transactions on Automatic Control, , p. 1-1 (2018) |
Permanent URL |
http://hdl.handle.net/2078.1/203197 |