Stability of Discrete Fractional Order State-space Systems

Abstract

In this article, the stability problem for discrete-time fractional order systems is considered. The discrete-time fractional order state-space model introduced by the authors in earlier works is recalled in this context. The proposed stability definition is adopted from one used for infinite dimensional systems. Using this definition, the main stability result is presented in the form of a simple stability condition for the fractional order discrete state-space system. This is one of the first few attempts to give the stability conditions for this type of system. The condition presented is conservative1 the method gives only sufficient conditions, and the stability areas obtained when using it are smaller than those obtained from numerical solutions of the system. The relationship between the eigenvalues of the system matrix and the poles of the fractional-order system transfer function is also discussed. The main observation in this respect is that a set of L poles is related to every eigenvalue of the system matrix.