Logarithmic integrals, interpolation bounds, and performance limitations in MIMO feedback systems

IEEE Transactions on Automatic Control

Volumn 45, Issue 6, 2000, Pages 1098-1115

  Chen, Jie ^a  

^a University of California ^*  (United States)

Author keywords

Bode integral relations; Design limitations; Linear multivariable systems; Nonminimum phase zeros; Performance limits; Time delays; Unstable poles

Indexed keywords

INTEGRAL EQUATIONS; INTERPOLATION; LINEAR SYSTEMS; PERTURBATION TECHNIQUES; POLES AND ZEROS; THEOREM PROVING; TIME VARYING SYSTEMS;

BODE INTEGRAL RELATIONS; INTERPOLATION BOUNDS; LINEAR MULTIVARIABLE SYSTEMS; LOGARITHMIC INTEGRALS; MULTI INPUT MULTI OUTPUT FEEDBACK SYSTEMS; NONMINIMUM PHASE ZEROS; TIME DELAYS;

CONTROL SYSTEM SYNTHESIS;

EID: 0034195692     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.863595     Document Type: Article

References (46)

1. J. A. Ball, I. Gohberg, and L. Rodman, Interpolation of Rational Matrix Functions, Operator Theory: Advances and Applications. Basel: Birkhäuser, 1990, vol. 45.
2. A. Bjorck and G. H. Golub, "Numerical methods for computing angles between linear subspaces," Math. of Computation, vol. 27, no. 123, pp. 579-594, July 1973.
3. H. W. Bode, Network Analysis and Feedback Amplifier Design. Princeton, NJ: Van Nostrand, 1945.
4. S. Boyd and C. A. Desoer, "Subharmonic functions and performance bounds in linear time-invariant feedback systems," IMA J. Math. Contr. Info., vol. 2, pp. 153-170, 1985.
5. B. C. Chang and J. B. Pearson, "Optimal disturbance reduction in linear multivariable systems," IEEE Trans. Automat. Contr., vol. 29, pp. 880-887, Oct. 1992.
6. B. M. Chen, A. Saberi, and P. Sannuti, "Explicit expressions for cascade factorization of general nonminimum phase systems," IEEE Trans. Automat. Contr., vol. 37, pp. 358-363, Mar. 1992.
7. J. Chen, "Sensitivity integral relations and design tradeoffs in linear multivariable feedback systems," IEEE Trans. Automat. Contr., vol. 40, pp. 1700-1716, Oct. 1995.
8. _, "Multivariable gain-phase and sensitivity integral relations and design tradeoffs," IEEE Trans. Automat. Contr., vol. 43, pp. 373-385, Mar. 1998.
9. _, "Sensitivity integrals and transformation techniques: A new perspective," IEEE Trans. Automat. Contr., vol. 42, pp. 1037-1042, July 1997.
10. _, "On logarithmic integrals and performance bounds for MIMO systems, Part I: Sensitivity integral inequalities," in Proc. 36th IEEE Conf. Decision Contr., San Diego, CA, Dec. 1997, pp. 3620-3625.
11. _, "On logarithmic complementary sensitivity integrals for MIMO systems," in Proc. Amer. Contr. Conf., Philadelphia, PA, June 1998.
12. _, "Intrinsic performance limits of linear feedback control," in Robustness in Identification and Control. ser. Lecture Notes in Contr. and Info. Sciences, A. Garulli, A. Tesi, and A. Vicino, Eds. London: Springer, 1999, vol. 245, pp. 227-241.
13. J. Chen and C. N. Nett, "Sensitivity integrals for multivariable discrete-time systems," Automatica, vol. 31, no. 8, pp. 1113-1124, Aug. 1995.
14. J. Chen, O. Toker, and L. Qiu, "Limitations on maximal tracking accuracy, part I: Tracking step signals," in Proc. 35th IEEE Conf. Decision Contr., Kobe, Japan, Dec. 1996, pp. 726-731.
15. J. C. Doyle, "Analysis of feedback systems with structured uncertainties," IEE Proc., vol. 129, Pt. D, no. 6, pp. 242-250, Nov. 1982.
16. J. S. Freudenberg and D. P. Looze, "Right half plane zeros and poles and design tradeoffs in feedback systems," IEEE Trans. Automat. Contr., vol. 30, pp. 555-565, June 1985.
17. _, "A sensitivity tradeoff for plants with time delay," IEEE Trans. Automat. Contr., vol. 32, pp. 99-104, Feb. 1987.
18. _, Frequency Domain Properties of Scalar and Multivariable Feedback Systems, Lecture Notes in Contr. and Info. Sciences, ser. Lecture Notes in Contr. and Info. Sciences. Berlin: Springer-Verlag, 1988, vol. 104.
19. J. S. Freudenberg, R. H. Middleton, and J. H. Braslavsky, "Inherent design limitations for linear sampled-data feedback systems," Int. J. Contr., vol. 61, no. 6, pp. 1387-1421, 1995.
20. ∞-error bounds," Int. J. Contr., vol. 39, pp. 1115-1193, 1984.
21. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore: Johns Hopkins Univ. Press, 1983.
22. G. C. Goodwin, D. Mayne, and J. Shim, "Tradeoffs in linear filter design," Automatica, vol. 31, no. 10, pp. 1367-1376, Oct. 1995.
23. M. Green and D. J. N. Limebeer, Linear Robust Control. Englewood Cliffs: Prentice Hall, 1995.
24. S. Hara and H. K. Sung, "Constraints on sensitivity characteristics in linear multivariable discrete-time control systems," Linear Algebra and its Appl., vol. 122/123/124, pp. 889-919, 1989.
25. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge Univ. Press, 1985.
26. T. Kato, Perturbation Theory for Linear Operators, 2nd ed. New York, NY: Springer-Verlag, 1984.
27. P. P. Khargonekar and A. Tannenbaum, "Non-Euclidean metrics and the robust stabilization of systems with parameter uncertainty," IEEE Trans. Automat. Contr., vol. 30, pp. 1005-1013, Oct. 1985.
28. P. Koosis, The Logarithmic Integral, II. London, England: Cambridge Univ. Press, 1992.
29. H. Kwakernaak and R. Sivan, "The maximally achievable accuracy of linear optimal regulators and linear optimal filters," IEEE Trans. Automat. Contr., vol. 17, pp. 79-86, Feb. 1972.
30. _, Linear Optimal Control Systems. New York, NY: Wiley-Interscience, 1972.
31. N. Levinson and R. M. Redheffer, Complex Variables. Baltimore: Holden-Day, 1970.
32. ∞-optimal control problems of the first kind," SIAM J. Contr. Optim., vol. 25, no. 6, pp. 1457-1493, Nov. 1987.
33. ∞ controller degree bounds," Linear Algebra and its Appl., vol. 98, pp. 347-386, 1988.
34. R. H. Middleton, "Trade-offs in linear control system design," Automatica, vol. 27, no. 2, pp. 281-292, Feb. 1991.
35. C. Mohtadi, "Bode's integral theorem for discrete-time systems," IEE Proc., vol. 137, Pt. D, no. 2, pp. 57-66, Mar. 1990.
36. M. Morari and E. Zafiriou, Robust Process Control. Englewood Cliffs, NJ: Prentice Hall, 1989.
37. L. Qiu and E. J. Davison, "Performance limitations of nonminimum phase systems in the servomechanism problem," Automatica, vol. 29, no. 2, pp. 337-349, 1993.
38. M. M. Seron, J. H. Braslavsky, and G. C. Goodwin, Fundamental Limitations in Filtering and Control. London: Springer-Verlag, 1997.
39. M. M. Seron, J. H. Braslavsky, P. V. Kokotovic, and D. Q. Mayne, "Feedback limitations in nonlinear systems: From Bode integrals to cheap control," in Proc. 36th IEEE Conf. Decision Contr., San Diego, CA, Dec. 1997, pp. 2067-2072.
40. H. K. Sung and S. Hara, "Properties of sensitivity and complementary sensitivity functions in single-input single-output digital control systems," Int. J. Contr., vol. 48, no. 6, pp. 2429-2439, 1988.
41. _, "Properties of complementary sensitivity function in SISO digital control systems," Int. J. Contr., vol. 48, no. 4, pp. 1283-1295, 1989.
42. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
43. J. E. Wall, Jr., J. C. Doyle, and C. A. Harvey, "Tradeoffs in the design of multivariable feedback systems," in Proc. 18th Allerton Conf., Oct. 1980, pp. 715-725.
44. G. Zames and B. A. Francis, "Feedback, minimax sensitivity, and optimal robustness," IEEE Trans. Automat. Contr., vol. 28, pp. 585-600, May 1985.
45. Z. Zhang and J. S. Freudenberg, "Loop transfer recovery for nonminimum phase plants," IEEE Trans. Automat. Contr., vol. 35, pp. 547-553, 1990.
46. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1996.