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This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I, new, general, necessary and sufficient stability conditions are introduced in a unified form for FD/FFD/NFFD-based systems. In Part II, an original, simple, analytical stability criterion is offered for FD-based systems, and the result is used to develop simple, efficient, numerical procedures for testing the asymptotic stability for FFD-based and, in particular, NFFD-based systems. Consequently, the so-called f -poles and f -zeros are introduced for FD-based system and their closed-loop stability implications are discussed.

bulletin of the polish academy of sciences. technical sciences

Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability