Eigenvalue Assignment for Positive Discrete-Time Linear Systems

This paper considers the problem of eigenvalue assignment for discrete-time positive systems by state feedback control law. The goal of the paper is to solve the stabilization problem of discrete-time positive systems under the constraint that the eigenvalues of the closed-loop system are placed in the desired location while maintaining the positivity structure. Although the problem of positive stabilization has been solved using LP and LMI methods, the problem of eigenvalue assignment with positivity constraints is complex and remains challenging. It has only been tackled for a restricted class of single-input discrete-time positive systems. This paper aims to provide a solution for the multi-input case. After a brief review of positive systems and their stability properties, spectral characteristics of stable positive discrete-time systems is analyzed and the eigenvalue assignment is achieved by solving a set of chain equations. Numerical examples are provided to support theoretical development.