Abstract
Given a reachable discrete-time linear system (A,b), the reachable set is a cone when a positive constraint is imposed on the input. The problem to be studied is the geometrical structure of the reachable set ℛ= cone(b, Ab, A2b,...) in terms of the spectrum ofA. In particular, conditions which ensure ℛ, or its closureR, is a polyhedral proper cone are derived. The impact of the given results on finite-time reachability and positive realizability is also discussed.
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Farina, L., Benvenuti, L. Polyhedral reachable set with positive controls. Math. Control Signal Systems 10, 364–380 (1997). https://doi.org/10.1007/BF01211552
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DOI: https://doi.org/10.1007/BF01211552