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IMA Journal of Mathematical Control and Information 1987 4(2):149-160; doi:10.1093/imamci/4.2.149
© 1987 by Institute of Mathematics and its Applications
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Approximating Reachable Sets for n-dimensional Linear Discrete Systems

JONATHAN E. GAYEK1 and MICHAEL E. FISHER2

1Department of Mathematics, Trinity University San Antonio, Texas, 78284, U.S.A.
2Department of Mathematics, University of Western Australia Nedlands, Western Australia 6009

We present a technique for approximating the reachable set from the origin for n-dimensional discrete-time linear systems subject to bounded control, where the state matrix is stable and diagonalizable. The procedure is based on decomposing the system into one- and two-dimensional subsystems for which the reachable set of each of the subsystems can be over-estimated by a polygon. These polygons are then used to create an n-dimensional polyhedron which contains the reachable set of the original system

Keywords: Reachable set; linear discrete systems; bounded control; decomposition.


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