By Topic

A necessary and sufficient minimality condition for uncertain 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)
Beck, C.L. ; Dept. of Gen. Eng., Illinois Univ., Urbana, IL, USA ; Doyle, John

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFTs) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist

Published in:

Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 10 )