Block circulant and block Toeplitz approximants of a class of spatially distributed systems-An LQR perspective

Orest V. Iftime*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)


In this paper block circulant and block Toeplitz long strings of MIMO systems with finite length are compared with their corresponding infinite-dimensional spatially invariant systems. The focus is on the convergence of the sequence of solutions to the control Riccati equations and the convergence of the sequence of growth bounds of the closed-loop generators. We show that block circulant approximants of infinite-dimensional spatially invariant systems reflect well the LQR behavior of the infinite-dimensional systems. An example of an exponentially stabilizable and exponentially detectable infinite-dimensional system is also considered in this paper. This example shows that the growth bounds of the Toeplitz approximants, as the length of the string increases, and the growth bound of the corresponding infinite-dimensional model, can be significantly different. On the positive side, we give sufficient conditions for the convergence of the growth bounds. (C) 2012 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)3098-3105
Number of pages8
Issue number12
Publication statusPublished - Dec-2012


  • Linear systems
  • Infinite-dimensional systems
  • LQR control
  • Spatially invariant systems
  • Spatially distributed systems

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