Performance Limits under Control Effort Constraints

  • Jie Chen
  • Shinji Hara
Part of the Trends in Mathematics book series (TM)


This paper presents some recent studies on performance limitations in optimal tracking and regulation control problems, in which objective functions of tracking error and regulated response, defined by integral square measures, are to be minimized jointly with the control effort, where the latter is measured by the plant input energy. The problems are solved explicitly by deriving analytical expressions for the best achievable performance. Other than the plant non-minimum phase zeros, time delays, and unstable poles, the results contain additional integral terms related to the gain characteristics of the plant and they reveal and quantify how the lightly damped poles, the anti-resonant zeros, and the bandwidth of the plant may all affect the performance. These effects are nonexistent when the control effort is not constrained, i.e., when it can be allowed to be infinite.


Performance limitation H2control Tracking and regulation Unstable poles and zeros 


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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Jie Chen
    • 1
  • Shinji Hara
    • 2
  1. 1.Department of Electrical EngineeringUniversity of CaliforniaRiversideUSA
  2. 2.Department of Information Physics and Computing Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan

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