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On a Modified Lur'e Problem

Thathachar, Lakshmi MA and Srinath, Mandyam D and Ramapriyan, HK (1967) On a Modified Lur'e Problem. In: IEEE Transactions on Automatic Control, 12 (6). pp. 731-740.


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This paper considers the problem of asymptotic stability in the large of an autonomous system containing a single nonlinearity. The nonlinear function is assumed to belong to several subclasses of monotonically increasing functions in the sector (0, K), and the stability criterion is shown to be of the form Re Z(j\omega) [G(j\omega) + \frac{1}{K}] - \frac{\delta'}{K} \geq 0 where the constant \delta' is equal to $Z(\infty) - Z_p(\infty)$ and $Z_p(s)$ is a Popov multiplier. The multiplier Z(s) can, in general, have complex conjugate poles and zeros and is thus more general than the type of multipliers obtained in previous results. The nonlinear functions considered are odd monotonic functions, functions with a power law restriction, and a new class of functions with restricted asymmetry having the property \mid \frac{f(\theta)}{f(-\theta)} \mid \leq c for all \theta. Unlike in certain earlier publications, no upper bound is placed on the derivative of the nonlinearity here. The results obtained can be used to establish stability in some cases even when the Nyquist plot of the linear part transfer function lies in all four quadrants and the nonlinearity is not necessarily odd. Furthermore, it is shown that the conditions on the multiplier and, consequently, those on the linear part can be relaxed as the feedback function approaches linearity.

Item Type: Journal Article
Publication: IEEE Transactions on Automatic Control
Publisher: IEEE
Additional Information: ©1967 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 08 Aug 2005
Last Modified: 19 Sep 2010 04:19
URI: http://eprints.iisc.ac.in/id/eprint/3490

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