H -Optimal parallel feedforward control using minimum gain

Ryan James Caverly, James Richard Forbes

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This letter presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system minimum phase by augmenting its output. The system output is perturbed the least amount possible by minimizing the gain of the parallel feedforward controller while ensuring the augmented system is minimum phase. This is done by minimizing the maximum singular value of a static parallel feedforward controller or the weighted H∞ norm of a dynamic parallel feedforward controller. Static and dynamic parallel feedforward controllers are synthesized using direct and indirect methods that involve bilinear matrix inequality constraints and are solved iteratively using linear matrix inequalities. The direct method enforces a minimum gain constraint directly on the augmented system, while the indirect method solves for an asymptotically stabilizing negative feedback controller that is inverted to obtain the parallel feedforward controller. Numerical examples are provided to demonstrate the effectiveness of the proposed controller synthesis methods.

Original languageEnglish (US)
Article number8382212
Pages (from-to)677-682
Number of pages6
JournalIEEE Control Systems Letters
Issue number4
StatePublished - Oct 2018

Bibliographical note

Funding Information:
Manuscript received March 2, 2018; revised May 7, 2018; accepted May 26, 2018. Date of publication June 12, 2018; date of current version June 26, 2018. This work was supported by the Natural Sciences and Engineering Research Council of Canada’s Postgraduate Scholarship Program. Recommended by Senior Editor F. Blanchini. (Corresponding author: Ryan James Caverly.) R. J. Caverly is with the Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: caverly@umich.edu).

Publisher Copyright:
© 2018 IEEE.


  • LMIs
  • Linear systems
  • Optimal control


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