Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction

IEEE Transactions on Automatic Control

Volumn 26, Issue 1, 1981, Pages 17-32

  Moore, Bruce C ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS, LINEAR;

EID: 0019533482     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1981.1102568     Document Type: Article

References (31)

1. B. C. Moore, “Singular value analysis of linear systems, parts I, II,” Dep. Elec. Eng., Univ. Toronto, Toronto, Ont., Syst. Contr. Rep. 7801 and 7802, July 1978; also in Proc. IEEE Conf. Dec. Contr., pp. 66–73.
2. R. E. Kalman, “Irreducible realizations and the degree of a rational matrix,” SIAM J. Appl. Math., vol. 13, no. 2, pp. 520–544, 1965.
3. ― “Algebraic structure of finite dimensional dynamical systems,” Proc. Nat. Acad Sci., U.S.A., vol. 54, pp. 1503–1508, 1965.
4. H. Hoteffing, “Analysis of a complex of statistical variables into principal components,” J. Edw. Psych., vol. 24, pp. 417–441, 498–520, 1933.
5. ― “Simplified calculation of principal components,” Psychometrica, vol. 1, 27–35, 1935.
6. G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numer. Math., vol. 14, pp. 403–420, 1970.
7. G. B. Crarbow et al., EISPACK Guide, Lecture Notes in Computer Science, 2nd ed., vol. 6. Berlin: Springer-Verlag, 1976.
8. A. P. Dempster, Elements of Continuous Multivariate Analysis. Reading, MA: Addison-Wesley, 1969.
9. V. C. Klema and A. J. Laub, “The singular value decomposition: Its computation and some applications, IEEE Trans. Automat. Contr., vol. AC-25, pp. 164–176, Apr. 1980.
10. J. H. Wilkinson, The Algebraic Eigenvalue Problem. New York: Oxford Univ. Press, 1965.
11. G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1967.
12. G. W. Stewart, Introduction to Matrix Computations. New York: Academic, 1973.
13. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems. Englewood Cliffs, NJ: Prentice-Hall, 1974.
14. G. Strang, Linear Algebra and its Applications. New York: Academic, 1976.
15. G. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods. for Mathematical Computations, Englewood Cliffs, NJ: Prentice-Hall, Hall, 1977.
16. B. C. Moore, “Principal component analysis in nonlinear systems: Preliminary results,” in Proc. 1979 IEEE Conf. Decision Contr., Fort Lauderdale, FL., Dec. 1979, pp. 1057–1060.
17. C. T. Mullis and R. A. Roberts, “Synthesis of minimum roundoff noise fixed point digital filters,” IEEE Trans. Circuits Syst., vol. CAS-23, pp. 551–562, Sept. 1976.
18. E. G. Lee and L. Marcus, Foundations of Optimal Control Theory. New York: Wiley, 1967.
19. R.W. Brockett, Finite Dimensional Linear Systems. New York: Wiley, 1970.
20. R. H. Bartels and G. W. Stewart, “Solution of the matrix equation AX + X B = C,” Commun. Ass. Comput. Mach., vol. 15, pp. 820–826, 1972.
21. B. Friedland, “Controllability index based on conditioning number,” Trans., ASME, J. Dynamic Syn., Measurement, Contr., pp. 444–445, Dec. 1975.
22. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 2nd ed. New York: Springer-Verlag, 1979.
23. L. Pernebo and L. M. Silverman, “Balanced systems and model reduction,” in Proc. 18th IEEE Conf. Decision Contr., Fort Lauderdale, FL, Dec. 12–14, 1979.
24. J. Rissanen, “Recursive identification of linear systems,” SIAM J. Contr. vol. 9, pp. 420–430, 1971.
25. H. P. Zeiger and J. McEwen, “Approximate linear realizations of given dimension via Ho's algorithm,” IEEE Trans. Automat. Contr., vol. AC-19, p. 153, 1974.
26. L. S. DeJong, “Numerical aspects of realization algorithms in linear systems theory,” Ph.D. dissertation, Eindhoven Univ. Technol., nol., Eindhoven, The Netherlands, 1975.
27. S. Kung, “A new identification and model reduction algorithm via singular value decompositions,” in Proc. 12th Ann. Asilomar Conf. Circuits, Syst. Comput., Nov. 1978.
28. D. A. Wilson, “Optimum solution of model-reduction problem,” Proc. IEEE, vol. 117, pp. 1161–1165, 1970.
29. ― “Model reduction for multivariable systems,” Int. J. Contr., vol. 20, 57–64, 1974.
30. J. D. Applevich, “Approximation of discrete linear systems,” Int. J. Contr., vol. 17, pp. 50–575, 1973.
31. P. J. M. Pinquet, “State space formulation of a class of model reduction methods,” M. Phil. thesis (supervised by K. Glover), Dep. Eng., Univ. Cambridge, Cambridge, England, 1978.