The set of stable polynomials of linear discrete systems: Its geometry

Automation and Remote Control

Volumn 63, Issue 7, 2002, Pages 1080-1088

  Nikolaev, Yu P ^a  

^a Institute of Electromechanics and Automation   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; DISCRETE TIME CONTROL SYSTEMS; GEOMETRY; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

AUXILIARY PLANES;

LINEAR CONTROL SYSTEMS;

EID: 84904240186     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016154714222     Document Type: Article

References (16)

1. Neimark, Yu.I., Ustoichivost' linearizovannykh sistem upravleniya (Stability of Linearized Control Systems). Leningrad: Leningr. Krasnoznam. Voen. Vozd. Inzh. Akad., 1949.
2. Jury, E.I. and Pavilidis, T., Stability and Aperiodicity Constraints for System Design, IEEE Trans. Circuit Theory, 1963, no. 10, pp. 137-141.
3. Fam, A.T. and Medich, J.S., A Canonical Parameter Space for Linear Systems Design, IEEE Trans. Autom. Control, 1978, vol. 23, no. 3, pp. 454-458.
4. Fam, A.T., The Volume of the Coefficient Space Stability Domain of Monic Polynomials, Proc. IEEE Int. Symp. Circuits and Systems, Portland, 1989, vol. 2, pp. 1780-1783.
5. Cohn, A., Über die Anzahl der Wurzeln einer Algebraischen Gleichung in einem Kreise, Math. Zeitschrift, 1922, vol. 14, pp. 110-148.
6. Ackerman, J., Robust Control, London: Springer-Verlag, 1993.
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. Vishnyakov, A.N. and Polyak, B.T., Design of Low-Order Controllers for Discrete Control Systems under Nonrandom Perturbations, Avtom. Telemekh., 2000, no. 9, pp. 112-119.
9. Kiselev, O.N. and Polyak, B.T., Minimization of Adjustments in Linear Discrete Systems with Low-Order Controllers, Avtom. Telemekh., 2001, no. 4, pp. 98-108.
10. Nikolaev, Yu.P., Symmetry and Other Properties of the Multidimensional Asymptotic Stability Domain of Linear Discrete Systems, Avtom. Telemekh., 2001, no. 11, pp. 109-120.
11. Hadwiger, H., Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Berlin: Springer, 1957. Translated under the title Lektsii ob ob"eme, ploshchadi poverkhnosti i izoperimetrii, Moscow: Nauka, 1966.
12. Hadwiger, H., Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Berlin: Springer, 1957. Translated under the title Lektsii ob ob"eme, ploshchadi poverkhnosti i izoperimetrii, Moscow: Nauka, 1966.
13. Kharitonov, V.L., Asymptotic Stability of the Equilibrium Position of a Family of Systems of Linear Differential Equations, Diff. Uravn., 1978, vol. 14, pp. 2086-2088.
14. Jury, E.I. Robustness of Discrete Systems, Avtom. Telemekh., 1990, no. 5, pp. 3-28.
15. Polyak, B.T. and Tsypkin, Ya.Z., Robust Stability of Linear Discrete Systems, Dokl. Akad. Nauk SSSR., 1991, vol. 316, no. 4, pp. 842-846.
16. Bose, N.K. and Zeheb, E., Kharitonov's Theorem and Stability Test of Multidimensional Digital Filters, IEE Proc. Pt. G., 1986, vol. 133, no. 4, pp. 187-190.