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Necessary and sufficient stability condition for arbitrarily switched linear systems from a data‐driven perspective
Author(s) -
Zhang Fan,
Söffker Dirk
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310232
Subject(s) - intersection (aeronautics) , perspective (graphical) , lyapunov function , mathematics , stability (learning theory) , function (biology) , set (abstract data type) , regular polygon , quadratic equation , matrix (chemical analysis) , space (punctuation) , control theory (sociology) , computer science , control (management) , engineering , geometry , artificial intelligence , physics , materials science , nonlinear system , quantum mechanics , machine learning , evolutionary biology , composite material , biology , programming language , aerospace engineering , operating system
In this paper, the problem of existence of Common Quadratic Lyapunov Function (CQLF) is handled in a data‐driven manner: instead of using mathematical models, a necessary and sufficient condition for existence of CQLF is established by direct use of measured system states. The paper shows that a CQLF exists if the intersection between the positive real space and the convex cone constructed by the data set transformed from the measured states using a suitable orthogonal matrix is not empty. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)