Robust Nonlinear PI Control

  • Randy A. Freeman
  • Petar Kokotović
Part of the Modern Birkhäuser Classics book series (MBC)


Thus far we have represented system uncertainty by a disturbance input w allowed to have an arbitrarily fast time variation. Its only constraint was the pointwise condition wW where W was some known set possibly depending on the state x and control u. We now address a more specific situation in which our system contains some uncertain nonlinearity φ(x). Suppose that all we know about φ is a set-valued map Φ(x) such that φ(x) ∈ Φ(x) for all xχ. We could assign wφ(x) and W(x) ≔ Φ(x) and proceed as in Chapters 3–6, but we would be throwing away a crucial piece of information about the uncertainty φ, namely, that φ(x) does not explicitly depend on time t. Our goal in this chapter is to illustrate how we can take advantage of this additional information to design less conservative robust controllers.


Lyapunov Function Tracking Error Controller Design Zero Dynamic Exogenous Disturbance 


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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Randy A. Freeman
    • 1
  • Petar Kokotović
    • 2
  1. 1.Department of Electrical and Computer EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

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