Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems
By Mikolaj Buslowicz, Andrzej Ruszewski. 2013
65 citations recorded by the source corpus.
In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/42950de744d1e977fe2d9414cc539ff37dc688c3
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In Computational Theory and Mathematics
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].”