Title :
Incremental positivity nonpreservation by stability multipliers
Author :
Kulkarni, Vishwesh V. ; Safonov, Michael G.
Author_Institution :
Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA
fDate :
1/1/2002 12:00:00 AM
Abstract :
It is proved that stability multipliers, such as Zames-Falb (1968) multipliers, Popov (1961) multipliers and RL/RC multipliers, known to preserve the 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, the continuity of the closed-loop system´s input-output relation may not be assured
Keywords :
closed loop systems; control nonlinearities; input-output stability; Popov multipliers; RL/RC multipliers; Zames-Falb multipliers; closed-loop system; incremental positivity nonpreservation; input-output relation continuity; integral quadratic constraint; monotone memoryless nonlinearities; nonlinear stability; stability multipliers; Acceleration; Attenuation measurement; Navigation; Nonlinear systems; Output feedback; Performance analysis; Stability; Sufficient conditions; Time varying systems; Upper bound;
Journal_Title :
Automatic Control, IEEE Transactions on
