Stability conditions for fractional discrete-time state-space systems with delays

Abstract

The stability problem of fractional discrete-time linear systems with delays has been analysed. The state-space model with a time shift in the difference has been considered. New necessary and sufficient conditions for the asymptotic stability and the practical stability have been established. The systems with only one matrix have been also analysed. It has been shown that such systems are asymptotically (practically) stable if all eigenvalues of the state matrix lie in the stability region of the complex plane.