Computer Aided Control System Design
  Polynomial Control Design Methods
Chair: Martin Hromcik 		Control Systems Society IEEE
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Abstract

This web page is maintained by the Action Group on Polynomial Methods for Control Design, which is part of the IEEE Control Systems Society Technical Committee on Computer Aided Control System Design. The motivation for setting up this group is to bring together specialists from various fields of science and engineering working with polynomials and polynomial matrices with (at least partial) focus on control system design and signal processing. This web page should help achieving this objective by collecting, sorting and presenting available and relevant information on polynomials, polynomial matrices and polynomial control design methods with special focus on computational tools.

Membership in the Action Group on Polynomial Methods

The membership in this group is free, but there is also no immediate financial benefit that the members can have. In simple terms, members of this group can have a name displayed in the "People" list and therefore a better chance to make other people aware of their research. This might turn out an advantage, for example, when preparing some formal joint research projects or invited sessions at conferences.

If you want to become a member, please contact the chair of the group.

Introduction to Polynomial Methods

Polynomial methods now constitute a mature bunch of theoretical and computational tools for control design and signal processing. The distinguished feature of this approach is a description of linear systems in a fractional form using transfer functions. For MIMO systems this concept generalizes to (left and right) fractions of polynomial matrices. The development of computational schemes then rests on polynomial matrix algebra. Major computational tools for control design are linear equations with polynomial matrices and (J-) spectral factorization of a polynomial matrix. On a numerical side, the problems lead to solving highly structured Toeplitz and block Teoplitz linear systems.

Polynomial methods can be viewed as an alternative approach to the well-established state-space methods relying on Lyapunov and Riccati equations. They provide essentially the same functionalities but use different theoretical and computational tools.

Purpose of this webpage

The major purpose of this webpage is to collect, sort and present available and relevant information on
  • CACSD tools capable of control-oriented computation with polynomial matrices
  • Research papers on diverse theoretical topics related to polynomial methods
  • Research groups and individual researchers working in related areas
  • Benchmarks for various control design routines based on manipulation with polynomial matrices, comparison with the state-space equivalents.
  • Courses, seminars and sessions at conferences
  • PhD and postdoctoral positions
  • Open problems
Everybody is encouraged to contribute to the content of this page, just send us the info you would like to have displayed here.
Number of visits: Last modified: January 4, 2005, by Zdenek Hurak