Title

Measuring Sparsity In Spatially Interconnected Systems

Abstract

The goal of this paper is to develop a mathematical framework to measure sparsity of state feedback controllers for spatially interconnected systems. We introduce a new algebra of infinite-dimensional matrices equipped with a matrix quasinorm which is defined using ℓq quasi-norm for 0 < q ≤ 1. When q = 0, the value of the matrix quasi-norm is equal to the maximum number of nonzero entries in rows or columns of a matrix. When 0 < q ≤ 1, the proposed matrix algebra forms a mathematical object so called q-Banach algebra, which is not a Banach algebra. We show that this matrix algebra is inverse-closed. Moreover, we prove that the unique solutions of Lyapunov and Riccati equations belong to this matrix algebra. We show that there exists a nonzero q for which the value of the matrix quasi-norm reflects a reasonable estimate for sparsity of a spatially decaying matrix. © 2013 IEEE.

Publication Date

1-1-2013

Publication Title

Proceedings of the IEEE Conference on Decision and Control

Number of Pages

1520-1525

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/CDC.2013.6760098

Socpus ID

84902324918 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84902324918

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