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Stability of nonlinear feedback systems in a Volterra representation
Author(s) -
Glass J. W.,
Franchek M. A.
Publication year - 2000
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 - 10.1002/1099-1239(200008)10:10<799::aid-rnc525>3.0.co;2-y
Subject(s) - control theory (sociology) , nonlinear system , volterra series , stability (learning theory) , mathematics , norm (philosophy) , frequency domain , kernel (algebra) , representation (politics) , linear system , class (philosophy) , computer science , mathematical analysis , control (management) , physics , quantum mechanics , artificial intelligence , machine learning , politics , political science , law , combinatorics
Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p ‐linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is non‐zero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity‐norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L ∞ . These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade‐off between performance and stability are considered for this class of nonlinear feedback systems. Copyright © 2000 John Wiley & Sons, Ltd.