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Limit cycle computation for describing function approximable nonlinear systems with box‐constrained parametric uncertainties
Author(s) -
Nataraj P. S. V.,
Barve J. J.
Publication year - 2005
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.999
Subject(s) - parametric statistics , nonlinear system , limit (mathematics) , limit cycle , describing function , function (biology) , mathematics , nonlinear element , computation , differentiable function , algorithm , computer science , control theory (sociology) , mathematical analysis , artificial intelligence , statistics , physics , quantum mechanics , evolutionary biology , biology , control (management)
We propose an algorithm to compute the limit cycle set of uncertain non‐rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non‐rational example with nonlinear parametric dependencies. Copyright © 2005 John Wiley & Sons, Ltd.