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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 576379, 7 pages
http://dx.doi.org/10.1155/2013/576379
Research Article

Control for Linear Positive Discrete-Time Systems

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan

Received 7 June 2013; Accepted 11 August 2013

Academic Editor: Wei-Shih Du

Copyright © 2013 Youmei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with 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 norm by using separating hyperplane theorem and Perron-Frobenius theorem for nonnegative matrices. We also consider 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.