Approximation properties of TP model forms and its consequences to TPDC design framework

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36 Citations (Scopus)


Tensor Product Distributed Compensation (TPDC) is a recently established controller design framework, that links TP model transformation and Parallel Distributed Compensation (PDC) framework. TP model transformation converts different models to a common representational form: the TP model form. The primary aim of this paper is to investigate the approximation capabilities of TP model forms, because the universal applicability of TPDC framework strongly relies on it. We point out that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. Consequently, in a class of control problems this property necessitates the usage of tradeoff techniques between the accuracy and the complexity of the TP form, which is easily feasible within the TPDC framework unlike in analytic models.

Original languageEnglish
Pages (from-to)221-231
Number of pages11
JournalAsian Journal of Control
Issue number3
Publication statusPublished - Sep 1 2007


  • Function decomposition
  • Linear Matrix Inequalities (LMI)
  • No-where denseness
  • Parallel Distributed Compensation (PDC) framework
  • TP model transformation
  • Tensor Product Distributed Compensation (TPDC) framework
  • Tensor product (TP) model form

ASJC Scopus subject areas

  • Control and Systems Engineering

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