By Topic

Co-Positive Lyapunov Functions for the Stabilization of Positive Switched 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

3 Author(s)
Blanchini, F. ; Dipt. di Mat. e Inf., Univ. di Udine, Udine, Italy ; Colaneri, P. ; Valcher, M.E.

In this paper, exponential stabilizability of continuous-time positive switched systems is investigated. For two-dimensional systems, exponential stabilizability by means of a switching control law can be achieved if and only if there exists a Hurwitz convex combination of the (Metzler) system matrices. In the higher dimensional case, it is shown by means of an example that the existence of a Hurwitz convex combination is only sufficient for exponential stabilizability, and that such a combination can be found if and only if there exists a smooth, positively homogeneous and co-positive control Lyapunov function for the system. In the general case, exponential stabilizability ensures the existence of a concave, positively homogeneous and co-positive control Lyapunov function, but this is not always smooth. The results obtained in the first part of the paper are exploited to characterize exponential stabilizability of positive switched systems with delays, and to provide a description of all the “switched equilibrium points” of an affine positive switched system.

Published in:

Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 12 )