Argument Increment Stability Criterion for Linear Delta Models

• Autorzy: Hofreiter M. , Zitek P.
• Języki publikacji: EN

Abstrakty

EN

Currently used stability criteria for linear sampled-data systems refer to the standard linear difference equation form of the system model. This paper presents a stability criterion based on the argument increment rule modified for the delta operator form of the sampled-data model. For the asymptotic stability of this system form it is necessary and sufficient that the roots of the appropriate characteristic equation lie inside a circle in the left half of the complex plane, the radius of which is inversely proportional to the sampling period. Therefore the argument increment of the system characteristic polynomial of an asymptotically stable delta model has to increase by 2pi n if this circle has been run around in the counter-clockwise direction. The criterion developed based on this principle permits not only the proof of the system stability itself, but also the approximation of the dominant roots of its characteristic equation.

Słowa kluczowe

EN

delta model; stability criterion; conformal mapping; delta operator; argument increment rule

PL

model delta; kryterium stabilności; mapowanie konformalne; operator delta

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 4
• Strony: 485--491
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

Hofreiter M.

• Czech Technical University in Prague, Faculty of Mechanical Engineering, Technicka 4, 166 07 Prague 6, Czech Republic

autor

Zitek P.

• Czech Technical University in Prague, Faculty of Mechanical Engineering, Technicka 4, 166 07 Prague 6, Czech Republic

Bibliografia

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• [3] Feuer A. and Goodwin G.C. (1996): Sampling in Digital Processing and Control.—Boston: Birkhäuser.
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• [5] Ogata K. (1995): Discrete-Time Control Systems.—Englewood Cliffs: Prentice-Hall.
• [6] Zítek P. (1990): Rate of stability criterion for discrete dynamic systems. — Acta Technica CSAV, Vol. 35, No. 1, pp. 83–92.
• [7] Zítek P. (2001): Mathematical and Simulation Models in Complex Domain. —Prague: CTU.
• [8] Zítek P. and Petrová R. (2001): Discrete approximation of anisochronic systems using delta transform. — Proc. Conf. Information Engineering and Process Control, IEPC, Prague: Masaryk Academy of Work, pp. 71–72.