On the absence of limit cycles in state-space digital filters with minimum L2-sensitivity

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 55, Issue 1, 2008, Pages 46-50

  Yamaki, Shunsuke ^a   Abe, Masahide ^a   Kawamata, Masayuki ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Controllability Gramian; Limit cycles; Minimum L2 sensitivity realization; Observability Gramian; State space digital filters

Indexed keywords

DIGITAL FILTERS; MATRIX ALGEBRA; OBSERVABILITY;

CONTROLLABILITY GRAMIAN; LIMIT-CYCLE; MINIMUM L2-SENSITIVITY REALIZATION; OBSERVABILITY GRAMIAN; STATE SPACE DIGITAL FILTERS;

LINEAR TRANSFORMATIONS;

EID: 57149132282     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2007.907757     Document Type: Article

References (10)

1. M. Kawamata and T. Higuchi, "On the absence of limit cycles in a class of state-space digital filters which contains minimum noise realizations," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, no. 4, pp. 928-930, Aug. 1984.
2. M. Kawamata and T. Higuchi, "A unified approach to the optimal synthesis of fixed-point state-space digital filters," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-33, no. 4, pp. 911-920, Aug. 1985.
3. 2-sensitivity minimization of linear state-space systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, no. 8, pp. 641-648, Aug. 1992.
4. 2-sensitivity for linear systems and two-dimensional state-space filters using general controllability and observability Gramians," IEEE Trans. Circuits Syst., vol. CAS-49, no. 9, pp. 1279-1289, Sep. 2002.
5. S. Yamaki, M. Abe, and M. Kawamata, "A closed form solution to L 2-sensitivity minimization of second-order state-space digital filters," in Proc. ISCAS'06, Kos, Greece, May 2006, pp. 5223-5226.
6. C. W. Barnes and A. T. Fam, "Minimum norm recursive digital filters that are free of overflow limit cycles," IEEE Trans. Circuits Syst. vol. CAS-24, no. 10, pp. 569-574, Oct. 1977.
7. W. L. Mills, C. T. Mullis, and R. A. Roberts, "Digital filter realizations without overflow oscillations," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-26, no. 4, pp. 334-338, Aug. 1978.
8. T. Ooba, "On companion systems with state saturation nonlinearity," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 12, pp. 1580-1584, Dec. 2003.
9. H. Kar and V. Singh, "Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: An LMI approach," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 51, no. 1, pp. 40-42, Jan. 2004.
10. V. Singh, "Modified form of liu-michel's criterion for global asymptotic stability of fixed-point state-space digital filters using saturation arithmetic," IEEE Trans. Circuits Syst. II, Exp. Briefs vol. 53, no. 12, pp. 1423-1425, Dec. 2006.