Stability of Discrete-Time Fractional Order Systems considered: An Approach Based on Stability of Discrete-Time Integer Order Time-Delay Systems

Abstract

In this paper the problem of stability of linear discrete-time fractional order systems is addressed. It was shown that some stability criteria for discrete time-delay systems could be applied with small changes to discrete fractional order state-space systems. Accordingly, simple conditions for the stability and robust stability of a particular class of linear discrete time-delay systems are derived. These results are modified and used for checking the stability of discrete-time fractional order systems. The systems under consideration involve time delays in the state and parameter uncertainties. The parameter uncertainties are assumed to be time-varying and norm bounded. New Lyapunov–Krasovskii functional is constructed to derive some delay dependent stability criteria. The proposed methods give both sufficient and necessary and sufficient stability conditions. Numerical examples have been worked out to show the applicability of the derived results.