Research Article Stabilization of Positive Linear Discrete-Time Systems by Using a Brauer’s Theorem

Copyright © 2014 Begoña Canto ́ 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. The stabilization problem of positive linear discrete-time systems (PLDS) by linear state feedback is considered. A method based on a Brauer’s theorem is proposed for solving the problem. It allows us to modify some eigenvalues of the system without changing the rest of them. The problem is studied for the single-input single-output (SISO) and for multi-input multioutput (MIMO) cases and sufficient conditions for stability and positivity of the closed-loop system are proved. The results are illustrated by numerical examples and the proposed method is used in stochastic systems. 1