Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

Raghu Venkataraman, Peter Seiler

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous-time, uncertain, gridded, linear parameter-varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency-domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst-case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst-case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.

Original languageEnglish (US)
Pages (from-to)953-975
Number of pages23
JournalInternational Journal of Robust and Nonlinear Control
Issue number3
StatePublished - Feb 1 2018

Bibliographical note

Funding Information:
The authors would like to thank Bin Hu, Sei Zhen Khong, Marcio Lacerda, Tamás Péni, Harald Pfifer, Zoltán Szabó, and Shu Wang for insightful discussions about this research. This work was supported by the National Science Foundation under grant NSF/CNS-1329390 entitled “CPS: Breakthrough: Collaborative Research: Managing Uncertainty in the Design of Safety-Critical Aviation Systems.”

Funding Information:
National Science Foundation, Grant/Award Number: NSF/CNS-1329390

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.


  • integral quadratic constraints
  • linear parameter-varying systems
  • robust control


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