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Spectral Bounds on the Solution of Linear Time‐Periodic Systems
Author(s) -
Benner Peter,
Denißen Jonas
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410412
Subject(s) - trigonometric functions , mathematics , nonlinear system , smoothness , chebyshev filter , rank (graph theory) , linear system , projection (relational algebra) , periodic function , function (biology) , stability (learning theory) , mathematical analysis , computer science , algorithm , combinatorics , geometry , physics , quantum mechanics , machine learning , evolutionary biology , biology
Linear time‐periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Stability of the solution may be proven by rigorous bounds on the solution. The key idea of this paper is to derive Chebyshev projection bounds on the original system by solving an approximated system. Depending on the smoothness of the original function, we formulate two upper bounds. The theoretical results are illustrated and compared to trigonometric spline bounds by means of two examples which include an anisotropic rotor‐bearing system. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)