**NONLINEAR
PHENOMENA IN COMPLEX SYSTEMS**

An Interdisciplinary Journal
* 2002, Vol.5, No.1, pp.44-50*

**Local Controllability for Differential Inclusions with Delay.**

*L.I. Minchenko and S.I. Sirotko*
In this work we prove new sufficient conditions for local controllability of
systems described with discrete approximations of differential inclusions
with delay

*
x(t+1) in F*_{t}(x(t),x(t-k)) t=0,1,...,N-1,

where *x* in **R**^{n}, *k* is a fixed positive
number, *F*_{t} are the
multifunctions from **R**^{n} x **R**^{n} into
**R**^{n} with closed
graphs. These sufficient conditions are based on Mordukhovich and
Kruger coderivatives of the multifunction *F*_{t} and allow to avoid
some restrictive assumptions with respect to the structure of the
system.

*Key words: *
control system, controllability, discrete inclusion,
multifunctionc

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Last updated: *March 24, 2002*