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Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems

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Abstract

We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors.

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Authors and Affiliations

  1. University of Groningen, Groningen, The Netherlands

    Ruth F. Curtain

  2. University of Bath, Bath, UK

    Mark R. Opmeer

Authors
  1. Ruth F. Curtain
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  2. Mark R. Opmeer
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Correspondence to Mark R. Opmeer.

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Curtain, R.F., Opmeer, M.R. Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems. Math. Control Signals Syst. 23, 101–115 (2011). https://doi.org/10.1007/s00498-011-0068-5

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  • DOI: https://doi.org/10.1007/s00498-011-0068-5

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