Abstract
This paper presents reachability results for a linear control system and arbitrary terminal pointsp inR n with controls constrained within a compact setU containing the origin. The well-known results forp=0 are then a special case of our results.
Geometric properties of the reachable set are presented and include: general containment properties which describe conditions that guarantee the inclusion of a reachable set in another reachable set; classification of the set of all pointsp that ensure the equivalence of two (different) reachable sets and the properties of this set.
The topological properties of the reachable set to a pointp depends on the control setU, the final pointp, and the location of the spectrum of the system in the complex plane. We characterize the geometric properties of the reachable set when the spectrum lies in the closed right-half plane, the open left-half plane, or a combination of both.
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Communicated by G. Leitmann
This work was supported in part by NSF Grant ECS-86-09586.
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Fashoro, M., Hàjek, O. & Loparo, K. Reachability properties of constrained linear systems. J Optim Theory Appl 73, 169–195 (1992). https://doi.org/10.1007/BF00940084
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DOI: https://doi.org/10.1007/BF00940084