The geometry of D-decomposition of a two-dimensional plane of arbitrary coefficients of the characteristic polynomial of a discrete system

Automation and Remote Control

Volumn 65, Issue 12, 2004, Pages 1904-1914

  Nikolaev, Yu P ^a  

^a Institute of Electromechanics and Automation   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY COEFFICIENTS; D-DECOMPOSITION; DISCRETE SYSTEM; TWO-DIMENSIONAL PLANE;

GEOMETRY; LINEAR EQUATIONS; LINEAR SYSTEMS; POLYNOMIALS; STABILITY; VOLUME MEASUREMENT;

TWO DIMENSIONAL;

EID: 84904240051     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:AURC.0000049876.54417.e6     Document Type: Article

References (17)

1. Neimark, Yu.I., Ustoichivost' linearizovannykh sistem upravleniya (Stability of Linearized Control Systems), Leningrad: LKVVIA, 1949.
2. Neimark, Yu.I., Dinamicheskie sistemy i upravlyaemye protsessy (Dynamic Systems and Control Processes), Moscow: Nauka, 1978.
3. Jury, E.I. and Pavilidis, T., Stability and Aperiodicity Constraints for System Design, IEEE Trans. Circuit Theory, 1963, no. 10. pp. 137-141.
4. Fam, A.T. and Medich, J.S., A Canonical Parameter Space for Linear Systems Design, IEEE Trans. Automat. Control, 1978, vol. 23, no. 3, pp. 454-458.
5. Ackerman, J., Robust Control: The Parameter Space Approach, London: Springer-Verlag, 2002.
6. Fam, A.T., The Volume of the Coefficient Space Stability Domain of Monic Polynomials, Proc. IEEE Int. Symp. Circuits and Systems, Portland, Oregon, 1989, vol. 2, pp. 1780-1783.
7. Polyak, B.T. and Halpern, M.E., Optimal Design for Discrete-Time Linear Systems via New Performance Index, Int. J. Adapt. Control Signal Proc., 2001, vol. 15, no. 2, pp. 129-152.
8. Nikolaev, Yu.P., Symmetry and Other Properties of Multidimensional Asymptotic Stability Domain of Linear Discrete Systems, Avtom. Telemekh., 2001, no. 11, pp. 109-120.
9. Nikolaev, Yu.P., The Geometry of a Set of Stable Polynomials of Linear Discrete Systems, Avtom. Telemekh., 2002, no. 7, pp. 44-54.
10. Cohn, A., Über die Anzahl der Wurzeln einer algebraischen Gleichung in Einem Kreise, Math. Zeitschrift, 1922, vol. 14, pp. 110-148.
11. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost' i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
12. Clark, C.W., A Delayed-Recruitment Model of Population Dynamics with an Application to Baleen Whale Populations, J. Math. Biology, 1976, no. 3, pp. 381-391.
13. Kuruklis, S.A., The Asymptotic Stability of x(n + 1) - ax(n) + bx(n - k) = 0, J. Math. Anal. Appl., 1994, vol. 188, pp. 719-731.
14. Lin, Y.-Z., Common Domain of Asymptotic Stability of a Family of Difference Equations, Appl. Math. E-Notes, 2001, no. 1, pp. 31-33.
15. Kipnis, M.M. and Nigmatulin, R.M., Stability of Certain Difference Equations with Two Delays, Avtom. Telemekh., 2003, no. 5, pp. 122-130.
16. Kipnis, M.M. and Nigmatulin, R.M., Stability of Three-Term Linear Equations with Two Delays Avtom. Telemekh., 2004, no. 11, pp. 25-39.
17. Dannan, F.M., The Asymptotic Stability of x(n + k) + ax(n) + bx(n - 1) = 0, J. Diff. Eq. Appl., 2004, vol. 10, no. 6, pp. 589-599.