On the non-optimality of linear quadratic gaussian balanced truncation for constrained order controller design

Ruben Merks, Mahmoodreza Mirzakhalili, Siep Weiland

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For model based control designs like boldsymbol{H}{2} and boldsymbol{H}{ boldsymbol{ infty}} optimal control, the controller order is typically equal to the model order. However, the synthesis and real-time implementation of these controllers may be hampered for models of large order due to computational limitations. Several closed-loop relevant order reduction techniques have been developed in order to overcome this problem. One technique is Linear Quadratic Gaussian (LQG) balanced truncation, which is closely related to LQG and boldsymbol{H}{2} optimal controller design. This paper demonstrates the non-optimality of this technique for constrained order boldsymbol{H}{2} optimal controller design. Furthermore, improvements to reduce the loss of performance as a result of truncation are proposed. These improvements can be applied to a large class of controller designs and order reduction techniques as well.

Original languageEnglish
Title of host publication2019 18th European Control Conference, ECC 2019
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)978-3-907144-00-8
Publication statusPublished - Jun 2019
Event18th European Control Conference (ECC 2019) - Naples, Italy
Duration: 25 Jun 201928 Jun 2019
Conference number: 18


Conference18th European Control Conference (ECC 2019)
Abbreviated titleECC 2019
Other18th European Control Conference (ECC 2019) (in cooperation with IFAC)
Internet address


  • H2 control
  • linear quadratic Gaussian control
  • linear quadratic Gaussian balanced truncation
  • constrained order H2 optimal controller design
  • controller designs
  • closed-loop relevant order reduction techniques
  • controller order
  • constrained order controller design


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