Zames-Falb multipliers for MIMO nonlinearities

Citation
Mg. Safonov et Vv. Kulkarni, Zames-Falb multipliers for MIMO nonlinearities, INT J ROBUS, 10(11-12), 2000, pp. 1025-1038
Citations number
16
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
ISSN journal
10498923 → ACNP
Volume
10
Issue
11-12
Year of publication
2000
Pages
1025 - 1038
Database
ISI
SICI code
1049-8923(200009/10)10:11-12<1025:ZMFMN>2.0.ZU;2-L
Abstract
In their celebrated 1968 paper on nonlinear stability, Zames and Falb deter mined a class of multipliers that preserve positivity of monotone SISO nonl inearities. They conjectured that their results might also hold for increme ntally positive, norm-bounded MIMO nonlinearities. In this note, we demonst rate that their conjecture regarding MIMO nonlinearities holds true only if a further restriction;is applied. Specifically, we show that it suffices e ither to restrict the nonlinearity to be the gradient of a convex real-valu ed function or to restrict the multiplier to be a real-valued function of f requency. Copyright (C) 2000 John Wiley & Sons, Ltd.