Authors:
Stefania Andersen
1
;
Elias August
2
;
Sigurdur Hafstein
1
and
Jacopo Piccini
2
Affiliations:
1
University of Iceland, Faculty of Physical Sciences, Dunhagi 5, 107 Reykjavik, Iceland
;
2
Reykjavik University, Department of Engineering, Menntavegur 1, 102 Reykjavik, Iceland
Keyword(s):
Switched Systems, Lyapunov Functions, Semidefinite Programming, Linear Programming, Visualisation Software.
Abstract:
For a switched system, of which each subsystem is linear, the exponential stability of the origin is equivalent to the existence of a common Lyapunov function (CLF) for all the subsystems. A popular approach to search for the latter is by means of solving a linear matrix inequality (LMI) using semidefinite programming (SDP). Another approach is to use linear programming (LP). The contribution of this work is twofold. First, we compare the SDP approach to the LP approach, with and without a certain preconditioning of system matrices. And, second, we present a software tool to visualise the conditions for a CLF. As the problem of investigating the stability of the origin is a very difficult one and sufficient and necessary conditions using the system matrices are only known for exponential stability of planar systems, a tool to visualise the original data in some meaningful form is potentially of great use for the full understanding of the problem.