L2-Induced norms and frequency gains of sampled-data sensitivity operators

IEEE Transactions on Automatic Control

Volumn 43, Issue 2, 1998, Pages 252-258

  Braslavsky, J H ^a   Middleton, R H ^b   Freudenberg, J S ^c  

^a University of California   (United States)

^b UNIVERSITY OF NEWCASTLE   (Australia)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Frequency response; Generalized sampled data holds; L2 induced norms; Robustness; Sampled data systems; Sensitivity analysis

Indexed keywords

FREQUENCY DOMAIN ANALYSIS; FREQUENCY RESPONSE; LINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); SENSITIVITY ANALYSIS; SYSTEM STABILITY; TIME DOMAIN ANALYSIS;

LINEAR TIME INVARIANT SYSTEMS; SAMPLED DATA SENSITIVITY OPERATORS;

SAMPLED DATA CONTROL SYSTEMS;

EID: 0031999540     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.661076     Document Type: Article

References (36)

1. P. Thompson, G. Stein, and M. Athans, "Conic sectors for sampled-data feedback systems," Syst. Contr. Lett., vol. 3, pp. 77-82, 1983.
2. P. Thompson, R. Daily, and J. Doyle, "New conic sectors for sampled-data feedback systems," Syst. Contr. Lett., vol. 7, pp. 395-404, 1986.
3. 2-induced norm of a sampled-data system," Syst. Contr. Lett., vol. 15, pp. 211-219, 1990.
4. G. Leung, T. Perry, and B. Francis, "Performance analysis of sampled data control systems," Automatica, vol. 27, no. 4, pp. 699-704, 1991.
5. Y. Yamamoto, "New approach to sampled-data systems: A function space method," in Proc. 29th Conf. Decision Contr., 1990, pp. 1882-1887.
6. B. Bamieh, J. Pearson, B. Francis, and A. Tannenbaum, "A lifting technique for linear periodic systems with applications to sampled-data control," Syst. Contr. Lett., vol. 17, pp. 79-88, 1991.
7. ∞ sampled-data control," IEEE Trans. Automat. Contr., vol. 37, pp. 418-435, 1992.
8. ∞ optimality criterion," Automatica, vol. 28, no. 1, pp. 45-54, 1992.
9. ∞-norm of sampled-data systems," Syst. Contr. Lett., vol. 21, pp. 163-172, 1993.
10. G. Dullerud and K. Glover, "Robust stabilization of sampled-data systems to structured LTI perturbations," IEEE Trans. Automat. Contr., vol. 38, pp. 1497-1508, 1993.
11. Y. Yamamoto, "A function space approach to sampled data control systems and tracking problems," IEEE Trans. Automat. Contr. vol. 39, pp. 703-713, 1994.
12. ∞ optimal sampled data control in continuous time systems," Int. J. Contr., vol. 56, p. 99, 1992.
13. P. Kabamba and S. Hara, "Worst-case analysis and design of sampled-data control systems," IEEE Trans. Automat. Contr., vol. 38, pp. 1337-1357, 1993.
14. ∞ control and filtering for sampled-data systems," IEEE Trans. Automat. Contr., vol. 38, pp. 1162-1175, 1993.
15. 2-induced norm for linear systems with jumps with applications to sampled-data systems," SIAM J. Contr. Optim., vol. 32, pp. 1128-1150, 1994.
16. P. Kabamba, "Control of linear systems using generalized sampled-data hold functions," IEEE Trans. Automat. Contr., pp. 772-783, 1987.
17. Y. Yamamoto and P. Khargonekar, "Frequency response of sampled-data systems," in Proc. 32nd Conf. Decision Contr., 1993, pp. 799-804;
18. also IEEE Trans. Automat. Contr., vol. 39, pp. 166-176, 1996.
19. ∞-norm of a sampled-data system," Syst. Contr. Lett., vol. 25, pp. 281-288, 1995.
20. Y. Yamamoto and M. Araki, "Frequency responses for sampled-data systems - Their equivalence and relationships," Linear Algebra Its Appl., vol. 206, pp. 1319-1339, 1994.
21. T. Chen and B. Francis, Optimal Sampled-Data Control Systems. New York: Springer-Verlag, 1995.
22. M. Araki, Y. Ito, and T. Hagiwara, "Frequency response of sampled-data systems," in Proc. 12th IFAC World Congr., 1993, pp. VII-289, 1993;
23. also Automatica, vol. 32, no. 4, pp. 483-497, 1996.
24. N. Sivashankar and P. Khargonekar, "Robust stability and performance analysis for sampled-data systems," IEEE Trans. Automat. Contr., vol. 39, pp. 58-69, 1993.
25. R. Middleton and J. Freudenberg, "Non-pathological sampling for generalized sampled-data hold functions," Automatica, vol. 31, 1995.
26. R. Middleton and J. Xie, "Non-pathological sampling for high order generalized sampled-data hold functions," in Proc. Automat. Contr. Conf., 1995.
27. T. Chen and B. Francis, "Input-output stability of sampled-data systems," IEEE Trans. Automat. Contr., vol. 36, pp. 50-58, 1991.
28. B. Francis and T. Georgiou, "Stability theory for linear time-invariant plants with periodic digital controllers," IEEE Trans. Automat. Contr., vol. 33, pp. 820-832, 1988.
29. J. Braslavsky, G. Meinsma, R. Middleton, and J. Freudenberg, "On a key sampling formula relating the Laplace and Z-transforms," Syst. Contr. Lett., vol. 29, pp. 181-190, 1997.
30. G. Goodwin and M. Salgado, "Frequency domain sensitivity functions for continuous time systems under sampled data control," Automatica, vol. 30, p. 1263, 1994.
31. J. Freudenberg, R. Middleton, and J. Braslavsky, "Inherent design limitations for linear sampled-data feedback systems," in Proc. Automat. Contr. Conf., June 1994, pp. 3227-3231;
32. also Int. J. Contr., vol. 61, no. 6, pp. 1387-1421, 1995.
33. R. Shenoy, D. Burnside, and T. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Process., vol. 42, pp. 2242-2256, 1994.
34. A. Balakrishnan, Applied Functional Analysis. New York: Springer-Verlag, 1981.
35. T. Hagiwara and M. Araki, "Robust stability of sampled-data systems under possibly unstable additive/multiplicative perturbations," in Proc. 1995 Automat. Contr. Conf., 1995, pp. 3893-3898.
36. C. Van Loan, "Computing integrals involving the matrix exponential," IEEE Trans. Automat. Contr., vol. 23, pp. 395-404, 1978.