Optimal FWL Design of State-Space Digital Systems with Weighted Sensitivity Minimization and Sparseness Consideration

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 39, Issue 5, 1992, Pages 365-377

  Li, Gang ^a   Gevers, Michel ^a   Anderson, Brian D O ^b   Perkins, Jane E ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--ALGORITHMS;

OPTIMAL FINITE WORD LENGTH (FWL) DESIGN; SCHUR REALIZATIONS; SPARSENESS CONSIDERATION; STATE-SPACE DIGITAL SYSTEMS; WEIGHTED SENSITIVITY MINIMIZATION;

ELECTRIC FILTERS, DIGITAL;

EID: 0026868371     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.139287     Document Type: Article

References (21)

1. C. T. Mullis and R. A. Roberts, “Filter structures which minimize roundoff noise in fixed-point digital filters,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing. pp. 505–508, 1976.
2. S. Y. Hwang, “Minimum uncorrelated unit noise in state-space digital filtering,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-25, pp. 273–281, Aug. 1977.
3. V. Tavsanoglu and L. Thiele, “Optimal design of state-space digital filters by simultaneous minimization of sensitivity and roundoff noise,” IEEE Trans. Circuits Syst., vol. CAS-31, pp. 884–888, Oct. 1984.
4. W. J. Lutz and S. Louis Hakimi, “Design of multi-input multi-output systems with minimum sensitivity,” IEEE Trans. Circuits Syst., vol. CAS-35, pp. 1114–1122, Sept. 1988.
5. L. Thiele, “On the sensitivity of linear state-space systems,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 502–510, May 1986.
6. R. H. Middleton and G. C. Goodwin, Digital Control and Estimation: A Unified Approach. Englewood Cliffs, NJ: Prentice Hall. 1990.
7. G. Li and M. Gevers, “Comparative study of finite wordlength effects in shift and delta operator parametrizations,” in Proc. 29th Conf. Decision and Control, pp. 954–959, Dec. 1990.
8. G. Li, “Finite precision aspects in the parametrizations of control, estimation, and filtering problems,” Ph.D. dissertation, Louvain Univ., Belgium, 1990.
9. L. Thiele, “Design of sensitivity and roundoff noise optimal state-space discrete systems,” Int. J. Circuit Theory Appl, vol. 12, pp. 39–46, 1984.
10. A. J. Laub, “Computing of balancing transformations,” in Proc. 29th IEEE Conf. JACC, vol. 1, Paper FA 8-E, 1980.
11. G. H. Golub and C. F. Van Loan, Matrix Computations. North Oxford Academic, 1989, second ed.
12. P. Van Dooren and M. Verhaegen, “On the use of unitary state-space transformations,” Contemporary Mathematics, vol. 47, pp. 447–463, 1985.
13. P. E. Mantey, “Eigenvalue sensitivity and state variable selection,” IEEE Trans. Automat. Contr., vol. AC-13, pp. 263–269, June 1968.
14. D. Williamson, “Roundoff noise minimization and pole-zero sensitivity in fixed-point digital filters using feedback,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1210–1220, Oct. 1986.
15. R. Bellman, Introduction to Matrix Analysis. New York: McGraw-Hill, 1970. second ed.
16. F. Neiss, Determinanten und Matrizen. Berlin, Germany: Springer-Verlag, 1967.
17. J. E. Perkins, U. Helmke, and J. B. Moore, “Balanced realizations via gradient flow techniques,” Syst. Contr. Lett., vol. 14. pp. 369–380, 1990.
18. M. Iwatsuki, M. Kawamata, and T. Higuchi, “Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems,” IEEE Trans. Circuits Syst., vol. 37. pp. 72–80, Jan. 1989.
19. M. Gevers and G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects. New York: Springer-Verlag, Communication and Control Engineering Series, to be published.
20. U. Helmke and J. B. Moore, “L2 sensitivity minimization of linear system representations via gradient flows,” submitted to J. Math. Syst., Estimation and Control, 1991.
21. R. A. Roberts and C. T. Mullis, Digital Signal Processing. Reading, MA: Addison Wesley, 1987.