Document Type
Article
Publication Date
2011
Abstract
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible cone, cic in short, and is in fact is replica of all realizations of positive functions of the same dimensions. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a by-product, this approach enables us to characterize systems which can be brought, through static output feedback, to be generalized positive.
Recommended Citation
D. Alpay and I. Lewkowicz. The positive real lemma and construction of all realizations of generalized positive rational functions. Systems and Control Letters, Volume 60 (2011), pp. 985-993.
Peer Reviewed
1
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons
Comments
NOTICE: this is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Systems and Control Letters, volume 60, in 2011. DOI: 10.1016/j.sysconle.2011.08.008
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