Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Root distribution of delta-operator formulated polynomials

Root distribution of delta-operator formulated polynomials

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Control Theory and Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

IEE
Published

Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden–Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden–Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.

Inspec keywords: matrix algebra; signal processing; stability; polynomials; discrete time systems

Other keywords: root distribution; Marden-Jury table; delta-operator formulated polynomials; scaling scheme; unit circle; characteristic equation; complex plane

Subjects: Discrete control systems; Signal processing theory; Signal processing and detection; Algebra; Algebra; Stability in control theory

References

    1. 1)
      • M. MANSOUR . (1993) Stability and robust stability of discrete-time systems in the δ-transform, Fundamentals of discrete-time systems: A tribute to Professor Eliahu I. Jury.
    2. 2)
      • T.S. HUANG . Stability of two-dimensional recursive filters. IEEE Trans. , 158 - 183
    3. 3)
      • G. LI , M. GEVERS . Roundoff noise minimization using delta-operator realizations. IEEE Trans. , 629 - 637
    4. 4)
      • E.I. JURY . (1986) Stability of multidimensional systems and related problems, Multidimensional systems, techniques, and applications.
    5. 5)
      • H. LEV-ARI , Y. BISTRITZ , T. KAILATH . Generalized Bezoutians and families of efficient zero-location procedures. IEEE Trans. , 170 - 186
    6. 6)
      • Y. BISTRITZ . Zero location with respect to the unit circle of discrete-time linear system polynomials. Proc. IEEE. , 1131 - 1142
    7. 7)
      • N.K. BOSE . Implementation of a new stability test for two-dimensional filters. IEEE Trans. , 117 - 120
    8. 8)
      • PREMARATNE, K.: `The equivalents of Schur–Colm minors for delta-operator formulated discrete-time systems', Proc. 1993 Pacific Rim Conf. Comm., Comp., Sig. Proc., PacRim'93, 1993, Victoria, BC, Canada.
    9. 9)
      • G. LIKOUREZOS . Prolog to High-speed digital signal processing and control. Proc. IEEE , 238 - 239
    10. 10)
      • REDDY, H.C., MOSCHYTZ, G.S., STUBERRUD, A.R.: `All pass function based stability test for delta-operator formulated discrete-time systems', Proc. 1995 IEEE Int. Symp. Circ. Syst., ISCAS'95, 1995, Seattle, WA, USA.
    11. 11)
      • D.D. SILJAK . Stability criteria for two-dimensional polynomials. IEEE Trans. , 185 - 189
    12. 12)
      • E.I. JURY . A note on the modified stability table for linear discrete time system. IEEE Trans. , 221 - 223
    13. 13)
      • B.D.O. ANDERSON , E.I. JURY , M. MANSOUR . Schwarz matrix properties for continuous and discrete time systems. Int. J. Control , 1 - 16
    14. 14)
      • E.I. Jury . (1964) , Theory and application of the .
    15. 15)
      • Y. BISTRITZ . Stability testing of two-dimensional discrete linear system polynomials by a two-dimensional tabular form. IEEE Trans. , 6 , 666 - 676
    16. 16)
      • H. FAN . Efficient zero location tests for delta-operator-based polynomials. IEEE Trans. , 5 , 722 - 727
    17. 17)
      • (1998) , MATLAB user's guide, Version 5.2.0.
    18. 18)
      • R.H. MIDDLETON , G.C. GOODWIN . (1990) , Digital control and estimation: A unified approach.
    19. 19)
      • H. FAN . A normalized Schur–Cohn stability test for delta-operator based polynomials. IEEE Trans. , 1606 - 1612
    20. 20)
      • K. PREMARATNE , A.S. BOUJARWAH . An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems. Multidimens. Syst. Signal Process , 287 - 312
    21. 21)
      • X. HU , E.I. JURY . On two-dimensional filter stability test. IEEE Trans. , 7 , 457 - 462
    22. 22)
      • MANSOUR, M., KRAUS, F.J., JURY, E.I.: `On robust stability of discrete-time systems using delta-operators', Proc. 1992 Auto. Cont. Conf., ACC'92, 1992, Chicago, IL, USA.
    23. 23)
      • B.D.O. ANDERSON , E.I. JURY . A simplified Schur–Cohn test. IEEE Trans. , 157 - 163
    24. 24)
      • TOUSET, S.: `A tabular algorithm for stability determination of delta-operator formulated discrete-time systems', 1998, MS Thesis, Univ. Miami, Dept. Elect. Comp. Eng., USA.
    25. 25)
      • G.C. GOODWIN , R.H. MIDDLETON , H.V. POOR . High-speed digital signal processing and control. Proc. IEEE , 240 - 259
    26. 26)
      • K. PREMARATNE , E.I. JURY . Tabular method for determining root distribution of delta-operator formulated real polynomials. IEEE Trans. , 352 - 355
    27. 27)
      • K. PREMARATNE , E.I. JURY . On the Bistritz tabular form and its relationship with the Schur–Cohn minors and inner determinants. J. Franklin Inst. , 165 - 182
    28. 28)
      • K. PREMARATNE , R. SALVI , N.R. HABIB , J.P. LE GALL . Delta-operator formulated discrete-time approximations of continuous-time systems. IEEE Trans. , 581 - 585
    29. 29)
      • E.I. JURY . Modified stability table for 2-D digital filters. IEEE Trans. , 116 - 119
    30. 30)
      • K. PREMARATNE , E.I. JURY . Application of polynomial array method to discrete-time system stability. IEE Proc. D. , 198 - 204
    31. 31)
      • E.I. JURY . A modified stability table for linear discrete systems. Proc. IEEE , 184 - 185
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_20000144
Loading

Related content

content/journals/10.1049/ip-cta_20000144
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address