Cart (Loading....) | Create Account
Close category search window
 

Verification of Aizerman's conjecture for a class of third-order systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Bergen, A.R. ; University of California, Berkeley, CA, USA ; Williams, I.

The second method of Lyapunov is used to validate Aizerman's conjecture for the class of third-order nonlinear control systems described by the following differential equation:tdot{e} + a_{2}ddot{e} + a_{1}dot{e} + a_{0}e + f(e)=0In this case, the stability of the nonlinear system may be inferred by considering an associated linear system in which the nonlinear functionf(e)is replaced byke. If the linear system is asymptotically stable fork_{1} < k < k_{2}, then the nonlinear system will be asymptotically stable in-the-large for anyf(e)for whichk_{1} < frac{f(e)}{e} < k_{2}.The Lyapunov function used to prove this result is determined in a straightforward manner by considering the physical behavior of the system at the extreme points of the allowable range ofk.

Published in:

Automatic Control, IRE Transactions on  (Volume:7 ,  Issue: 3 )

Date of Publication:

Apr 1962

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.