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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

2 2013

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

Stanisławski R., Latawiec K. J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 2

353--361

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.

Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems

Stanisławski R., Latawiec K. J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 2

363--370

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 of the paper, new necessary and sufficient stability conditions have been given in a unified form for FD, FFD and NFFD-based systems. Part II offers a new, simple, ultimate stability criterion for FD-based systems. This gives rise to the introduction of new definitions of the so-called f-poles and f-zeros for FD-based systems, which are used in the closed-loop stability analysis for FD-based systems and, approximately, for FFD/NFFD-based ones.