| Contents |
| The Riemann-Liouville, Caputo and Gr\"{u}nwald-Letnikov fractional order difference operators are discussed and used to state and solve the local controllability problem of local controllability in a finite number of steps of $h$-difference nonlinear control systems with $n$
fractional orders. There are used three types of forward differences:
the fractional Riemann-Liouville type difference, fractional Caputo type difference and fractional Gr\"{u}nwald-Letnikov type difference.
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.
\section{Acknowledgment}
The work was supported by Bialystok University of Technology grant G/WM/3/2012. The project was supported
by the founds of National Science Center granted on the
bases of the decision number DEC-2011/03/B/ST7/03476. |
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