By Topic

The Positivstellensatz and nonexistence of common quadratic Lyapunov functions

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)
Davis, J.M. ; Dept. of Math., Baylor Univ., Waco, TX, USA ; Eisenbarth, G.

We provide an algorithm for establishing the nonexistence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonex-istence question is equivalent to the emptiness of an associated semi-algebraic set. The celebrated Positivstellensatz from real algebraic geometry provides a complete characterization of when this set is empty. Finally, we obtain the desired certificates of set emptiness using sum of squares programming.

Published in:

System Theory (SSST), 2011 IEEE 43rd Southeastern Symposium on

Date of Conference:

14-16 March 2011