LMI-based Stability and H_∞ Performance Analysis of Discrete-time Positive Systems

Abstract

This paper is concerned with the stability and H_∞ performance analysis of discrete-time positive systems. In the literature, it is shown that the stability and H_∞ performance of continuous-time positive systems can be characterized by LMIs with diagonal Lyapunov matrices. Recently, new LMIs allowing asymmetric matrix solutions have been reported as well. In this paper, by means of the Perron-Frobenius theorem, we first show that the Schur stability of a given positive matrix is equivalent to the Hurwitz stability of an appropriately constructed Metzler matrix. Then, we secondly prove that we can construct a continuous-time positive system preserving the stability and H_∞ norm of the original discrete-time positive system. By applying existing results to the resulting continuous-time positive systems, we can readily obtain useful LMIs for the stability and H_∞ performance analysis of discrete-time positive systems.