Optimal LPV control with hard constraints

Andrew White, Guoming Zhu, Jongeun Choi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ2 to ℓ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H performance criterion is also considered as well. Controllers with a guaranteed ℓ2 to ℓ gain and a guaranteed H performance (ℓ2 to ℓ2 gain) are a special family of mixed H2=H controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ℓ2 to ℓ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ2 to ℓ gain and >H performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

Original languageEnglish
Pages (from-to)148-162
Number of pages15
JournalInternational Journal of Control, Automation and Systems
Issue number1
Publication statusPublished - 2016 Feb 1

Bibliographical note

Publisher Copyright:
© 2016, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications


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