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Dual-lattice theorems in the geometric approach

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Abstract

A one-to-one correspondence is shown to exist between the lattice of all self-bounded (A, ℬ)-controlled invariants contained in ℒ and the lattice of all self-hidden (A, ℒ)-conditioned invariants containing ℬ. This correspondence, stated herein as the main dual-lattice theorem, allows a straightforward derivation of the universal bounds of the lattices, particularly when additional constraints are imposed, such as to contain a given subspace ℘ for the elements of the former lattice and to be contained in a given subspace ℒ for the elements of the latter. Then, two further minor dual-lattice theorems, dual to each other, are presented, and some connections and applications of the new theory to standard control and observation problems are briefly discussed.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Florida, Gainesville, Florida

    G. Basile (Professor)

  2. Department of Electronics, Computers, and Systems, University of Bologna, Bologna, Italy

    G. Marro (Professor)

Authors
  1. G. Basile
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  2. G. Marro
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Communicated by G. Leitmann

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Basile, G., Marro, G. Dual-lattice theorems in the geometric approach. J Optim Theory Appl 48, 229–244 (1986). https://doi.org/10.1007/BF00940671

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  • DOI: https://doi.org/10.1007/BF00940671

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