Abstract: The reachable set bounding estimation for distributed
delay systems with disturbances is a new problem. In this paper,we
consider this problem subject to not only time varying delay and
polytopic uncertainties but also distributed delay systems which is
not studied fully untill now. we can obtain improved non-ellipsoidal
reachable set estimation for neural networks with time-varying delay
by the maximal Lyapunov-Krasovskii fuctional which is constructed
as the pointwise maximum of a family of Lyapunov-Krasovskii
fuctionals corresponds to vertexes of uncertain polytope.On the other
hand,matrix inequalities containing only one scalar and Matlabs
LMI Toolbox is utilized to give a non-ellipsoidal description of the
reachable set.finally,numerical examples are given to illustrate the
existing results.