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Hankel/Toeplitz matrices and the static output feedback stabilization problem

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Abstract

The static output feedback (SOF) stabilization problem for general linear, continuous-time and discrete-time systems is discussed. A few novel necessary and sufficient conditions are proposed, and a modified SOF stabilization problem with performance is studied. For multiple-input single-output (or single-input multiple-output) systems the relation with a class of Hankel matrices, and their inverses, in the continuous-time case and with a class of Toeplitz matrices, in the discrete-time case, is established. These relationships are used to construct conceptual numerical algorithms. Finally, it is shown that, in the continuous-time case, the problem can be recast as a concave–convex programming problem. A few worked out examples illustrate the underlying theory.

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Authors and Affiliations

  1. Electrical and Electronic Engineering Department, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom

    Alessandro Astolfi

  2. Dip. di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Patrizio Colaneri

Authors
  1. Alessandro Astolfi
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  2. Patrizio Colaneri
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Correspondence to Alessandro Astolfi.

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Astolfi, A., Colaneri, P. Hankel/Toeplitz matrices and the static output feedback stabilization problem. Math. Control Signals Syst. 17, 231–268 (2005). https://doi.org/10.1007/s00498-005-0157-4

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  • DOI: https://doi.org/10.1007/s00498-005-0157-4

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