Mathematics of Control, Signals and Systems

, Volume 17, Issue 4, pp 231–268 | Cite as

Hankel/Toeplitz matrices and the static output feedback stabilization problem

  • Alessandro Astolfi
  • Patrizio Colaneri


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.


Static output feedback Stabilization Hankel matrices Toeplitz matrices 


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© Springer-Verlag London Limited 2005

Authors and Affiliations

  1. 1.Electrical and Electronic Engineering DepartmentImperial College LondonLondonUnited Kingdom
  2. 2.Dip. di Elettronica e InformazionePolitecnico di MilanoMilanoItaly

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