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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Local controllability of nonlinear discrete-time fractional order systems

1 / E. Pawłuszewicz2

1Faculty of Computer Science, Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland

2Faculty of Mechanical Engineering, Bialystok University of Technology, 45C Wiejska St., 15-351 Białystok, Poland

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Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences. Volume 61, Issue 1, Pages 251–256, ISSN (Print) 0239-7528, DOI: 10.2478/bpasts-2013-0024, May 2013

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The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

Keywords : fractional difference operator; fractional difference initial value problem; nonlinear fractional order system; linear approximation; controllability problem

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