Asymptotic properties of discrete linear fractional equations

In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a comple...

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Bibliographic Details
Published in:Bulletin of the Polish Academy of Sciences. Technical sciences 2019-01, Vol.67 (4), p.749-759
Main Authors: Anh, P T, Babiarz, A, Czornik, A, Niezabitowski, M, Siegmund, S
Format: Article
Language:English
Subjects:
Asymptotic properties
caputo equation
Computer science
Control theory
Dimensional stability
Discrete time systems
Invariants
Investigations
linear discrete-time fractional systems
Liouville equations
Mathematical analysis
Mathematics
riemann-liouville equation
stability
volterra convolution equation
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Summary:In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo and Riemann-Liouvile equations and we also show an explicit formula for the solution of systems of time-invariant Caputo equations.
ISSN:0239-7528
2300-1917
DOI:10.24425/bpasts.2019.130184