CSD Approach to Stabilization Control and H2 Optimal Control

  • Mi-Ching Tsai
  • Da-Wei Gu
Part of the Advances in Industrial Control book series (AIC)


For a control system under investigation, an important design objective is to find a controller such that the closed-loop system satisfies a set of desired specifications. Furthermore, it is desirable to characterize all such controllers which achieve the required specifications. To accomplish this task, the required specifications can be first formulated into an adequate performance index, and then one can minimize the index to obtain sought controllers. This chapter presents a unified approach for solving a fairly general class of control synthesis problems by employing chain scattering-matrix descriptions and coprime factorizations. In particular, robust stabilization problems and the optimal H 2 control will be discussed in this chapter, respectively. The H (sub)optimal control problem can also be solved along the same approach which will be presented in the next chapter.


Output Estimation Optimal Controller Linear Quadratic Regulator Full Column Rank Linear Fractional Transformation 
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  1. 1.
    Boulet B, Francis BA (1998) Consistency of open-loop experimental frequency-response date with coprime factor plant models. IEEE Trans Autom Control 43:1680–1691CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Chen J (1997) Frequency-domain tests for validation of linear fractional uncertain models. IEEE Trans Autom Control 42:748–760CrossRefzbMATHGoogle Scholar
  3. 3.
    Doyle JC, Glover K, Khargonekar PP, Francis BA (1989) State-space solutions to standard H 2 and H control problems. IEEE Trans Autom Control 34:831–847CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Evans WR (1948) Graphical analysis of control systems. Trans AIEE 67:547–551Google Scholar
  5. 5.
    Francis BA, Zames G (1987) On H -optimal sensitivity theory for SISO feedback systems. IEEE Trans Autom Control 29:9–16CrossRefMathSciNetGoogle Scholar
  6. 6.
    Glover K, Doyle JC (1988) State-space formulae for all stabilizing controllers that satisfy an H -norm bounded and relations to risk sensitivity. Syst Control Lett 11:167–172CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Green M, Limebeer DJN (1995) Linear robust control. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  8. 8.
    Kimura H (1987) Directional interpolation approach to H optimization and robust stabilization. IEEE Trans Autom Control 32:1085–1093CrossRefzbMATHGoogle Scholar
  9. 9.
    Kimura H (1995) Chain-scattering representation, J-lossless factorization and H control. J Math Syst Estim Control 5:203–255zbMATHGoogle Scholar
  10. 10.
    Kimura H (1997) Chain-scattering approach to H control. Birkhäuser, BostonCrossRefzbMATHGoogle Scholar
  11. 11.
    Kimura H, Okunishi F (1995) Chain-scattering approach to control system design. In: Isidori A (ed) Trends in control: an European perspective. Springer, BerlinGoogle Scholar
  12. 12.
    Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley, New YorkzbMATHGoogle Scholar
  13. 13.
    MacFarlane AGJ, Postlethwaite I (1977) Characteristic frequency functions and characteristic gain functions. Int J Control 26:265–278CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Nyquist H (1932) Regeneration theory. Bell Syst Tech J 11:126–147CrossRefzbMATHGoogle Scholar
  15. 15.
    Rosenbrock HH (1974) Computer aided control system design. Academic, New YorkGoogle Scholar
  16. 16.
    Safonov MG, Athans M (1977) Gain and phase margin for multiloop LQG regulators. IEEE Trans Autom Control 22:173–178CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Smith RS, Doyle JC (1992) Model validation: a connection between robust control and identification. IEEE Trans Autom Control 37:942–952CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Tsai MC, Tsai CS, Sun YY (1993) On discrete-time H control: a J-lossless coprime factorization approach. IEEE Trans Autom Control 38:1143–1147CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Zames G (1981) Feedback and optimal sensitivity: model reference transformation, multiplicative seminorms, and approximated inverse. IEEE Trans Autom Control 26:301–320CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Zames G, Francis BA (1983) Feedback, minimax sensitivity, and optimal robustness. IEEE Trans Autom Control 28:585–601CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Zhou K, Doyle JC, Glover K (1995) Robust and optimal control. Prentice Hall, Upper Saddle RiverGoogle Scholar
  22. 22.
    Zhou K, Doyle JC (1998) Essentials of robust control. Prentice Hall, Upper Saddle RiverGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Mi-Ching Tsai
    • 1
  • Da-Wei Gu
    • 2
  1. 1.Department of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan
  2. 2.Department of EngineeringUniversity of LeicesterLeicesterUK

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