Title :
Incremental positivity non-preservation by stability multipliers
Author :
Kulkarni, V.V. ; Safonov, Michael G.
Author_Institution :
Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA
Abstract :
It is proved that stability multipliers such as Zames-Falb multipliers, Popov multipliers and RL/RC multipliers, known to preserve positivity of monotone memoryless nonlinearities, do not, in general, preserve their incremental positivity. Our result implies that stability results based on these multipliers should be interpreted with caution since without incremental positivity, continuity of the closed-loop system´s input-output relation may not be assured
Keywords :
Fourier transforms; feedback; stability; Popov multipliers; RL/RC multipliers; Zames-Falb multipliers; closed-loop system; continuity; incremental positivity nonpreservation; input-output relation; integral quadratic constraint; nonlinear stability; stability analysis; stability multipliers; Convolution; Feedback; Fourier transforms; Signal mapping; Stability analysis;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980064