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

By R. Stanisławski, Krzysztof J. Latawiec. 2013

80 citations recorded by the source corpus.

. 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.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/9c512b5e37afe47f511a444c7877b57cc40e34b0

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In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

The -Transform Method and Delta Type Fractional Difference Operators (2015, background): “In the case of the Grünwald-Letnikov-type fractional operator our results are similar to those in [11, 13, 14].”