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Zames-Falb multipliers for MIMO nonlinearities

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2 Author(s)
Safonov, M.G. ; Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA ; Kulkarni, V.V.

Zames and Falb (1968) determined a class of multipliers that preserve positivity of monotone SISO nonlinearities. They conjectured that their results might also hold for incrementally positive, norm-bounded MIMO nonlinearities. In this note, we demonstrate that their conjecture regarding MIMO nonlinearities holds true only if a further restriction is applied. Specifically, we show that it suffices either to restrict the nonlinearity to be the gradient of a convex real-valued function or to restrict the multiplier to be a real-valued function of frequency

Published in:

American Control Conference, 2000. Proceedings of the 2000  (Volume:6 )

Date of Conference:

2000