A non-normality measure of the condition number for monitoring and control

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 119, Issue 2, 1997, Pages 217-222

  Huh, Kunsoo ^a   Stein, Jeffrey L ^b  

^a Hanyang University   (South Korea)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0342553551     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.2801236     Document Type: Article

References (27)

1. Bauer, F. L., 1963, “Optimally Scaled Matrices,” Numerische Mathematik, Vol. 5, pp. 73-87.
2. Becker, P. W., and Jensen, F., 1977, Design of Systems and Circuits for Maximum Reliability or Maximum Production Yield, McGraw-Hill Book Co.
3. Berger, W. A., Perry, R. J., and Sun, H. H., 1989, “Eigenvalue Sensitivity in Multivariable Systems,” Proceedings IEEE International Conference on Systems Engineering, CH2767-2, pp. 433-436.
4. Byers, R., and Nash, S., 1989, “Approaches to Robust Pole Assignment,” International Journal of Control, Vol. 49, No. 1, pp. 97-117.
5. Changsheng, J., 1991, “New Method of Robust Pole Assignment by Output Feedback,” IEEE Proceedings-D, Vol. 138, No. 2, March, pp. 172-176.
6. Forsythe, G. E., and Moler, D. B., 1967, Computer Solution of Linear Algebraic Systems, Prentice-Hall, Englewood Cliffs, NJ.
7. Gilbert, E. G., 1984, “Conditions for Minimizing the Norm Sensitivity of Characteristic Roots,” IEEE Transactions on Automatic Control, Vol. 29, No. 7, pp. 658-661.
8. Gill, P. E., Murphy, W., and Wright, M. H., 1981, Practical Optimization, Academic Press, New York.
9. Henrici, P., 1962, “Bounds for Iterates, Inverse, Spectral Variation and Fields of Values of Nonnormal Matrices,” Numerische Mathematik, Vol. 4, pp. 24-40.
10. Huh, K., and Stein, J. L„ 1993a, “A Quantitative Performance Index for Model-based Monitoring Systems,” American Control Conference, San Francisco, CA, pp. 917-924. (Also accepted for publication in the ASME Journal of Dynamic Systems, Measurement, and Control).
11. Huh, K., and Stein, J. L., 1993b, “Well-Conditioned Observer Design for Model-Based Monitoring Systems,” American Control Conference, San Francisco, CA, pp. 1959-1965. (Also accepted for publication in the ASME Journal of Dynamic Systems, Measurement, and Control).
12. Huh, K., 1992, “A Design Procedure for Model-based Monitoring Systems for Machine Monitoring,” Ph.D. thesis, The University of Michigan.
13. Kautsky, J., Nichols, N. K., and Van Dooren, P., 1985, “Robust Pole Assignment in Linear State Feedback,” International Journal of Control, Vol. 41, No. 5 pp. 1129-1155.
14. Keel, L. H., and Battacharyya, S. P., 1990, “State-Space Design of Low-Order Stabilizers,” IEEE Transactions on Automatic Control, Vol. AC-35, No. 2, pp. 182-186.
15. Lau, H., and Jensen, K. F., 1985, “Evaluation of Changeover Control Policies by Singular Value Analysis-Effects of Scaling,” AIChE Journal, Vol. 31, No. 1, pp. 135-146.
16. Maciejowski, J. M., 1989, Multivariable Feedback Design, Addison-Wesley, New York.
17. Nguyen, T. C Barton, G. W., Perkins, J. D., and Johnston, R. D., 1988, “A Condition Number Scaling Policy for Stability Robustness Analysis,” AIChE Journal, Vol. 34, No. 7, pp. 1200-1206.
18. Noble, B„ and Daniel, J. W., 1977, Applied Linear Algebra, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.
19. Pang, G. K. H., and MacFarlane, A. G. J., 1987, An Expert Systems Approach to Computer-Aided Design of Multivariable Systems, Vol. 89, Lecture Notes in Control and Information Sciences, Springer-Verlag.
20. Ruhe, A., 1975, “On the Closedness of Eigenvalues and Singular Values for Almost Normal Matrices,” Linear Algebra and Its Applications, Vol. 11, pp. 8794.
21. Skelton, R. E., and Wagie, D. A., 1984, “Minimal Root Sensitivity in Linear Systems,” Journal of Guidance, Vol. 7, No. 5, pp. 570-574.
22. Sobel, K. M., Banda, S. S., and Shapiro, E. Y., 1988, “Robust Modalized Observer with Flight Control Application,” Proceedings for the 27th Conference on Decision and Control, Austin, Texas, pp. 1018-1019.
23. Spurgeon, S. K., 1990, “Pole Placement Extensions for Multivariable Systems-A Survey,” American Control Conference, Vol. 2, pp. 1660-1665.
24. Stein, J. L., and Park, Y., 1989, “Steady-State, Optimal State and Input Observer for Discrete Stochastic Systems,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 3, pp. 121-127, June.
25. Stewart, G. W., 1973, Introduction to Matrix Computations, Academic Press, New York and London.
26. Van Der Sluis, A., 1969, “Condition Numbers and Equilibration of Matrices,” Numerical Mathematics, Vol. 14, pp. 14-23.
27. Wilkinson, J. H., 1965, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford