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Robust linear-quadratic minimization

Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 5)

Keywords

Performance Index Riccati Equation Bounded Variation Terminal State Extremal Solution 
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References

  1. [1]
    J.B. Moore and B.D.O. Anderson, "Extensions of quadratic minimization theory, I: Finite time results", Int. J. Control, Vol. 7, No. 5, 1968, pp. 465–472.Google Scholar
  2. [2]
    D.H. Jacobson, "Totally singular quadratic minimization problems", IEEE Trans. Automatic Control, Vol. AC-16, 1971, pp. 651–658.Google Scholar
  3. [3]
    B.D.O. Anderson, "Partially singular linear-quadratic control problems", IEEE Trans. Automatic Control, Vol. AC-18, 1973, pp. 407–409.Google Scholar
  4. [4]
    B.P. Molinari, "Nonnegativity of a quadratic functional", SIAM J. Control, Vol. 13, 1975, pp. 792–806.Google Scholar
  5. [5]
    W.A. Coppel, "Linear-quadratic optimal control, Proc. Roy. Soc. Edin., Vol. 73A, 1974-5, pp. 271–289.Google Scholar
  6. [6]
    D.J. Clements, B.D.O. Anderson and P.J. Moylan, "Matrix inequality solution to linear-quadratic singular control problems", IEEE Trans. Automatic Control, Vol. AC-22, 1977, pp. 55–57.Google Scholar
  7. [7]
    D.H. Jacobson and J.L. Speyer, "Necessary and sufficient conditions for singular control problems: a limit approach", J. Math. Anal. Appl., Vol. 34, 1971, pp. 239–266.Google Scholar
  8. [8]
    R.W. Brockett, Finite Dimensional Linear Systems, John Wiley, New York, 1970.Google Scholar
  9. [9]
    P.A. Faurre, "Sur les points conjugués en commande optimale", C.R. Acad. Sci., Ser. A, Vol. 266, 1968, pp. 1294–1296.Google Scholar
  10. [10]
    I.M. Gelfand and S.V. Fomin, Calculus of Variations, Prentice-Hall, N.J., 1963.Google Scholar
  11. [11]
    B.D.O. Anderson and P.J. Moylan, "Spectral factorization of a finite-dimensional nonstationary matrix covariance", IEEE Trans. Automatic Control, Vol. AC-19, 1974, pp. 680–692.Google Scholar
  12. [12]
    B.D.O. Anderson and P.J. Moylan, "Synthesis of linear time-varying passive networks", IEEE Trans. Circuits and Systems, Vol. CAS-21, 1974, pp. 678–687.Google Scholar
  13. [13]
    D.G. Luenberger, Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Co. Inc., London, 1973.Google Scholar
  14. [14]
    B.D.O. Anderson and D.J. Clements, "Robust linear-quadratic minimization", J. Math. Anal. Appl., to be published.Google Scholar
  15. [15]
    J.C. Willems, "Least squares stationary control and the algebraic Riccati equation", IEEE Trans. Automatic Control, Vol. AC-16, 1971, pp. 621–234.Google Scholar
  16. [16]
    D.J. Clements and B.D.O. Anderson, "Extremal solutions of Riemann-Stieltjes inequalities of linear optimal control", IEEE Trans. Automatic Control, Vol. AC-22, 1976, pp. 139–140.Google Scholar

Copyright information

© Springer-Verlag 1978

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