H∞ Control for Linear Positive Discrete‐Time Systems

Youmei Zhang, Qingling Zhang and Tamaki Tanaka

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: This paper is concerned with H∞ control for linear positive discrete‐time systems. Positive systems are characterized by nonnegative restriction on systems’ variables. This restriction results in some remarkable results which are available only for linear positive systems. One of them is the celebrated diagonal positive definite matrix solutions to some existed well‐known results for linear systems without nonnegative restriction. We provide an alternative proof for criterion of H∞ norm by using separating hyperplane theorem and Perron‐Frobenius theorem for nonnegative matrices. We also consider H∞ control problem for linear positive discrete‐time systems via state feedback. Necessary and sufficient conditions for such problem are presented under controller gain with and without nonnegative restriction, and then the desired controller gains can be obtained from the feasible solutions.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/576379

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:576379

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().