H mixed sensitivity minimization for stable infinite-dimensional plants subject to convex constraints

Oguzhan Cifdaloz, Armando Rodriguez

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


This paper shows how convex optimization may be used to design near-optimal finite-dimensional compensators for stable linear time invariant (LTI) infinite dimensional plants. The infinite dimensional plant is approximated by a finite dimensional transfer function matrix. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixedsensitivity H optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated optimization problem from an infinite dimensional optimization problem involving a search over stable real-rational transfer function matrices in H to a finite-dimensional optimization problem involving a search over a finite-dimensional space. In addition to solving weighted mixed sensitivity H control system design problems, it is shown how subgradient concepts may be used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Illustrative examples are provided.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Number of pages6
StatePublished - 2005
Event2005 American Control Conference, ACC - Portland, OR, United States
Duration: Jun 8 2005Jun 10 2005


Other2005 American Control Conference, ACC
Country/TerritoryUnited States
CityPortland, OR


  • Convex optimization
  • H mixed sensitivity
  • Infinite dimensional
  • Time domain constraints

ASJC Scopus subject areas

  • Control and Systems Engineering


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