@article{dec906cfb61d487fb709d8b2b3358000,
title = "Absolute Stability Criteria for Multiple Slope-Restricted Monotonic Nonlinearities",
abstract = "Absolute stability criteria such as the classical Popov criterion guarantee stability for a class of sector-bounded nonlinearities. Although the sector restriction bounds the admissible class of the nonlinearities, the local slope of the nonlinearity may be arbitrarily large. In this paper we derive absolute stability criteria for multiple slope-restricted time-invariant monotonic nonlinearities. Like the Popov criterion, in the single-input/single-output case our results provide a simple graphical interpretation involving a straight line in a modified Popov plane.",
author = "Haddad, {Wassim M.} and Vikram Kapila",
note = "Funding Information: In recent research [lo], [16], [18] a new absolute stability criterion for locally slope-restricted nonlinearities involving a simple modification to the Popov multiplier was developed. Specifically, it was shown in [ 181 that replacing the Popov multiplier Z(.s ) = 1 + -Y.s by the new multiplier 1 + TsP' and requiring the frequency domain condition + (1 + Ss-')G(.s) be positive real, where Manuscript received January 30, 1993; revised April 18, 1994. This research was supported in part by the National Science Foundation Research Grants ECS-9109558 and ECS-9350181. The authors are with the School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150 USA. IEEE Log Number 9407219.",
year = "1995",
month = feb,
doi = "10.1109/9.341811",
language = "English (US)",
volume = "40",
pages = "361--365",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",
}