Describing the H set in the controller parameters space

Cristiano Spelta, Elena N. Gryazina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


The aim of this paper is to give an instrument for describing the regions in the controller parameter space such that the H-norm of the closed loop transfer function of a given system is less than a prescribed level. In this note we consider a particular family of linear control systems, comprising also plant with PID controller. We show that for such systems the problem can be easily tackled with the analysis of non-homogeneous quadratic forms in the parameters space, so that first the general L region can be well approximated, and then the H subregion distinguished. We present a method for both the description of such a region and of its border, and the proposed approach is valid for continuous-time and discrete-time systems. In case of two parameters controller a nice graphical analysis may be performed. Finally some examples are provided in order to explore the technique proposed.

Original languageEnglish
Title of host publication2007 European Control Conference, ECC 2007
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages8
ISBN (Electronic)9783952417386
Publication statusPublished - 2007
Externally publishedYes
Event2007 9th European Control Conference, ECC 2007 - Kos, Greece
Duration: 2 Jul 20075 Jul 2007

Publication series

Name2007 European Control Conference, ECC 2007


Conference2007 9th European Control Conference, ECC 2007


  • H specifications
  • linear systems
  • low-order controllers
  • parameter space


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