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State estimation for linear impulsive differential systems
through polyhedral techniques
The paper is devoted to the state estimation problem in control
theory under uncertainty.
The approach for estimating the reachable sets of the
linear impulsive differential systems is presented.
The reachable sets are approximated by the ones for
special discrete time systems.
The degree of convergence is established.
The families of external and internal polyhedral
(parallelepiped-valued and parallelotope-valued) estimates of
the reachable sets of the auxiliary systems are introduced.
Evolution of estimates is determined by systems of recurrence relations.
The families which ensure the exact representations of the reachable sets
of the auxiliary systems as well as the families
of the touching and tight estimates are found.
This technique gives the possibility to construct the
guaranteed estimates (including $\epsilon$-touching and
$\epsilon$-tight ones) for the reachable sets
of the primary systems.
The results of numerical simulations are presented.