By Topic

Necessary and sufficient conditions for absolute stability: the case of second-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
$33 $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)
Margaliot, M. ; Dept. of Theor. Math., Weizmann Inst. of Sci., Rehovot, Israel ; Langholz, G.

We consider the problem of absolute stability of linear feedback systems in which the control is a sector-bounded time-varying nonlinearity. Absolute stability entails not only the characterization of the "most destabilizing" nonlinearity, but also determining the parametric value of the nonlinearity that yields instability of the feedback system. The problem was first formulated in the 1940s, however, finding easily verifiable necessary and sufficient conditions for absolute stability remained an open problem all along. Recently, the problem gained renewed interest in the context of stability of hybrid dynamical systems, since solving the absolute stability problem implies stability analysis of switched linear systems. In this paper, we introduce the concept of generalized first integrals and use it to characterize the "most destabilizing" nonlinearity and to explicitly construct a Lyapunov function that yields an easily verifiable, necessary and sufficient condition for absolute stability of second-order systems.

Published in:

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:50 ,  Issue: 2 )