Rational approximation of L1-optimal controller

  • Yoshito Ohta
  • Hajime Maeda
  • Shinzo Kodama
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 183)


This paper studies the L1-optimal control problem for SISO systems with rational controllers. It is shown that the infimal achievable norm with rational controllers is as small as that with irrational controllers. Also a way to construct a rational suboptimal controller is studied.


Dual Problem Duality Theorem Disturbance Rejection Minimal Realization Rational Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F.M. Callier and C.A. Desoer, ‘An algebra of transfer functions of distributed linear time-invariant systems.’ IEEE Trans. Circuits Syst., vol.CAS-25, pp.651–662, 1978.CrossRefMathSciNetGoogle Scholar
  2. [2]
    M.A. Dahleh and J.B. Pearson, ‘l1 optimal feedback controllers for MIMO discrete-time systems,’ IEEE Trans. Automat. Contr., vol.AC-32, pp.314–322, 1987.CrossRefGoogle Scholar
  3. [3]
    M.A. Dahleh and J.B. Pearson, ‘L1-optimal compensators for continuous-time systems,’ IEEE Trans. Automat. Contr., vol.AC-32, pp.889–895, 1987.CrossRefGoogle Scholar
  4. [4]
    C.A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Orlando, Florida: Academic Press, 1975.zbMATHGoogle Scholar
  5. [5]
    D.G. Luenberger, Optimization by Vector Space Methods, New York: John Wiley & Sons, 1969.zbMATHGoogle Scholar
  6. [6]
    R.T. Rockafellar, Convex Analysis, Princeton, New Jersey: Princeton, 1970.zbMATHGoogle Scholar
  7. [7]
    M. Vidyasagar, ‘Optimal rejection of persistent bounded disturbances,’ IEEE Trans. Automat. Contr., vol.AC-31, pp.527–534, 1986.CrossRefMathSciNetGoogle Scholar
  8. [8]
    M. Vidyasagar, ‘Further results on the optimal rejection of persistent bounded disturbances, Part II: Continuous-time case,’ preprint.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Yoshito Ohta
    • 1
  • Hajime Maeda
    • 2
  • Shinzo Kodama
    • 2
  1. 1.Department of Mechanical Engineering for Computer-Controlled MachineryOsaka UniversitySuita, OsakaJapan
  2. 2.Department of Electronic EngineeringOsaka UniversitySuita, OsakaJapan

Personalised recommendations