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

The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty

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

4 Author(s)
Pluymers, B. ; Dept. of Electr. Eng., Katholieke Univ., Leuven, Belgium ; Rossiter, J.A. ; Suykens, J.A.K. ; De Moor, B.

In this paper the concept of maximal admissable set (MAS), introduced by Gilbert et al. (1991) for linear time-invariant systems, is extended to linear systems with polytopic uncertainty under linear state feedback. It is shown that by constructing a tree of state predictions using the vertices of the uncertainty polytope and by imposing state and input constraints on these predictions, a polyhedral robust invariant set can be constructed. The resulting set is proven to be the maximal admissable set. The number of constraints defining the invariant set is shown to be finite if the closed loop system is quadratically stable (i.e. has a quadratic Lyapunov function). An algorithm is also proposed that efficiently computes the polyhedral set without exhaustively exploring the entire prediction tree. This is achieved through the formulation of a more general invariance condition than that proposed in Gilbert et al. (1991) and by the removal of redundant constraints in intermediate steps. The efficiency and correctness of the algorithm is demonstrated by means of a numerical example.

Published in:

American Control Conference, 2005. Proceedings of the 2005

Date of Conference:

8-10 June 2005

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.