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Research Article
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Singular Perturbation Problems Using Indefinite Lyapunov Functions

Year 1997, Volume: 10 Issue: 2, 64 - 78, 31.12.1997

Ayhan Albostan , Ahmet Özek

Abstract

With a dynamic system of differential
equations consisting of many variables the singular perturbation methods are of
great importance.

Keywords

indefinite Lyapunov function singular perturbation two-time-scale system nonlinear systems

References

  • [1] K. Kl]alilHassan, "Aron/mea7'S>'ıtem$, /'renrtce-7'fa//", UpperSaddIeRiver, N. J., 1996.
  • [2] M. Vİdyasagar, "Nonlmear Systems Anatysis", Prentice-HaIl, ini:. Englewood Cliffs, N. J., 1996.
  • [3] A. Halanay, ". Stability Theorems of Gradstem-Klimusev-Krcfvovski Type for coupled Differenlial-Difference and Difference Eijuations With Small Delays, (leclure on). Cali. On Qualitative Theory of DiffereMial Eyuations", pp 27-31. August 1984, Szeged, Hımgaıy.
  • [4] T. Yoshizawa, "Staiility Theory by Lyapumv's Seconıl Method", TheîAatb. Soc. ofjapan, 1966.
  • [5] N. Rouche, L. Habets, M. Laloıv, "Stabilily Theory by Lyapunov's Direct Method. Springeı", VewYork, 1977.
  • [6] J. d'Azzo John and H. Houpls Constantine, "Liııear Control System", Mc Graw-Hill Book Company, New York, 1990.
  • [7]. V. Kerte'sz, "Application of indefinite Lyapunov fanction for stability investigations", ZAMMVo\. 63., pp 66-68, 1983.
  • [8] V. Kerte'sz, "Seperation oflarge and small solutions using indefinite Lyapunov functions", ZAMM, Vol. 64. pp 366-367, 1984.
  • [9] M. A. Aizerman and F. R. Gantmacher, "Absolule Slabiiily of Regülatör Systems", Holden- Day, Inc. San Francisco, 1964.
  • [10] K.KhaliI Hassan, "Stability Analysis of Nonlinear Multiparameter Singulariy Perturbed Systems. " IEEE Trans. Onautomalic Control .40-32(3), pp 260-263, March 1987.
  • [11] P.V. Kokotovic, Hassan K.K.haliI and J.O'Reilly, "Sngular Pmurbatmns Methods m Cantrol, analysis anrfOerigr, ", Academic Press, New York, 19Ç6.
  • [12] H. Ch0w Joe and V. Kokotovic Petar, '-Two-Time-ScaIe Feedback Design of a CIass of Nnn'inear Systems", IEEE Trcms. On. A-utomalic CoMrol, Vol. AC-23, No. 3, June 1978.

Singular Perturbation Problems Using Indefinite Lyapunov Functions

Year 1997, Volume: 10 Issue: 2, 64 - 78, 31.12.1997

Ayhan Albostan , Ahmet Özek

Abstract

With a dynamic system of differential equations consisting of many variables the singular perturbation methods are of great importance.

Keywords

indefinite Lyapunov function singular perturbation two-time-scale system nonlinear systems

References

  • [1] K. Kl]alilHassan, "Aron/mea7'S>'ıtem$, /'renrtce-7'fa//", UpperSaddIeRiver, N. J., 1996.
  • [2] M. Vİdyasagar, "Nonlmear Systems Anatysis", Prentice-HaIl, ini:. Englewood Cliffs, N. J., 1996.
  • [3] A. Halanay, ". Stability Theorems of Gradstem-Klimusev-Krcfvovski Type for coupled Differenlial-Difference and Difference Eijuations With Small Delays, (leclure on). Cali. On Qualitative Theory of DiffereMial Eyuations", pp 27-31. August 1984, Szeged, Hımgaıy.
  • [4] T. Yoshizawa, "Staiility Theory by Lyapumv's Seconıl Method", TheîAatb. Soc. ofjapan, 1966.
  • [5] N. Rouche, L. Habets, M. Laloıv, "Stabilily Theory by Lyapunov's Direct Method. Springeı", VewYork, 1977.
  • [6] J. d'Azzo John and H. Houpls Constantine, "Liııear Control System", Mc Graw-Hill Book Company, New York, 1990.
  • [7]. V. Kerte'sz, "Application of indefinite Lyapunov fanction for stability investigations", ZAMMVo\. 63., pp 66-68, 1983.
  • [8] V. Kerte'sz, "Seperation oflarge and small solutions using indefinite Lyapunov functions", ZAMM, Vol. 64. pp 366-367, 1984.
  • [9] M. A. Aizerman and F. R. Gantmacher, "Absolule Slabiiily of Regülatör Systems", Holden- Day, Inc. San Francisco, 1964.
  • [10] K.KhaliI Hassan, "Stability Analysis of Nonlinear Multiparameter Singulariy Perturbed Systems. " IEEE Trans. Onautomalic Control .40-32(3), pp 260-263, March 1987.
  • [11] P.V. Kokotovic, Hassan K.K.haliI and J.O'Reilly, "Sngular Pmurbatmns Methods m Cantrol, analysis anrfOerigr, ", Academic Press, New York, 19Ç6.
  • [12] H. Ch0w Joe and V. Kokotovic Petar, '-Two-Time-ScaIe Feedback Design of a CIass of Nnn'inear Systems", IEEE Trcms. On. A-utomalic CoMrol, Vol. AC-23, No. 3, June 1978.
There are 12 citations in total.

Details

Subjects Electrical Engineering
Journal Section Research Articles
Authors

Ayhan Albostan

Ahmet Özek This is me

Publication Date December 31, 1997
Acceptance Date July 1, 1997
Published in Issue Year 1997 Volume: 10 Issue: 2

Cite

APA Albostan, A., & Özek, A. (1997). Singular Perturbation Problems Using Indefinite Lyapunov Functions. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, 10(2), 64-78.
AMA Albostan A, Özek A. Singular Perturbation Problems Using Indefinite Lyapunov Functions. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi. December 1997;10(2):64-78.
Chicago Albostan, Ayhan, and Ahmet Özek. “Singular Perturbation Problems Using Indefinite Lyapunov Functions”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi 10, no. 2 (December 1997): 64-78.
EndNote Albostan A, Özek A (December 1, 1997) Singular Perturbation Problems Using Indefinite Lyapunov Functions. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 10 2 64–78.
IEEE A. Albostan and A. Özek, “Singular Perturbation Problems Using Indefinite Lyapunov Functions”, Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, vol. 10, no. 2, pp. 64–78, 1997.
ISNAD Albostan, Ayhan - Özek, Ahmet. “Singular Perturbation Problems Using Indefinite Lyapunov Functions”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 10/2 (December1997), 64-78.
JAMA Albostan A, Özek A. Singular Perturbation Problems Using Indefinite Lyapunov Functions. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi. 1997;10:64–78.
MLA Albostan, Ayhan and Ahmet Özek. “Singular Perturbation Problems Using Indefinite Lyapunov Functions”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, vol. 10, no. 2, 1997, pp. 64-78.
Vancouver Albostan A, Özek A. Singular Perturbation Problems Using Indefinite Lyapunov Functions. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi. 1997;10(2):64-78.
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