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LYAPUNOV METODU iLE FARK DENKLEMLERiNiN KARARLILIGININ BELiRLENMESi

Year 2007, Issue: 013, 31 - 38, 15.06.2007

Abstract

As it is known, Lyapunov method was used for stability of the solution of the generalized energy fonctions, but recently, this method is used for stability of the difference equations. In this study, We have shown how to used Lyapunav method for the stability of the difference equations and this method has been applied some examples.

References

  • [1]. S, Yoden and M, Nomura. Finite-time Lyapunov stability analysis and its application to atmospheric predictability, Journal of the Atmospheric Seciences. VoL50, Iss.11; p. 1531, (1993).
  • [2]. H, Komurcugil and 0, kukrer. Lyapunov-based control for three-phase PWM ACIDC voltage-source converters, IEEE Transactions on Power Electronics, Vo1.13, Iss.5; p.801, (1998).
  • [3]. Gen-Qi Xu and Siu Pang Yung. Lyapunov stability of abstract nonlinear dynamic system in Banach space, IMAjournal of mathematical control and information, Vol. 20, Iss 1, p. 105, (2003).
  • [4]. M. Yoshimasa. The Lyapunov stability of the N-soliton solutions in the Lax hieerarshy of the Benjamin- Ono equation, Journal of Mathematical Physics, VoL 47, Iss. 10; p. 1, (2006).
  • [5]. I, Karafyllis. Non-uniform robust global asymptotic stability for discrete-time systems and appliations to numerical analysis, IMA Journal of Mathematical Control and Information, Vol. 23, Iss. 1; p. 11, (2006).
  • [6]. C.H.Lee. solution Bounds of the Continuous and Discrete Lyapunov Matrix equations, Journal of Optimization Theory and applications, VoL 120, Iss.3; p. 559, (2004).
  • [7]. Shufang Xu and M Cheng. On the Solvability fort he mixed-type Lyapunov equation, IMA journal of Applied Mathematics, VoL71, Iss. 2; p. 287, (2006).
  • [8]. Richard C. H. Lee, C.W. Wong, Cheng-Zhong Xu, L.H.Yim and S.P. Yung. A Lyapunov-type condition for robust feedback stability of delay control systems, IMA journal of Mathematical control and Information, VoL 23, Iss. 1; p. 97, (2006).
  • [9]. E. Moulay and W. Perruquetti. Finite time stability of differential inclusions, IMA journal of Mathematical control and Information, Vol. 22, Iss. 4; p. 465, (2005).
  • [10]. Oliver Mason and Robert Shorten. On common quadratic Lyapunov functions for stable discretetime LTI systems, IMAjournal of Applied Mathematics, Vo1.69, Iss. 3; p. 271, (2004)
  • [11]. Elaydi saber, 1996, An Introduction to Difference Equations, springer, 31.

LYAPUNOV METODU iLE FARK DENKLEMLERiNiN KARARLILIGININ BELiRLENMESi

Year 2007, Issue: 013, 31 - 38, 15.06.2007

Abstract

Bilindigi gibi, Lyapunov metodu, genellestirilrnis bir enerji fonksiyonunun coznmlerinin kararhhgi icin kullarnr. Fakat son zamanlarda fark denklem sistemlerinin cozumlerinin kararhligr icinde kullarulrnaya baslanmisnr. Bu cahsmada, Lyapunov metodu kullarularak fark denklemlerinin kararhhginm nasil belirlendigi ele ahndi ve bazi ornek problemlere uygulandi.

References

  • [1]. S, Yoden and M, Nomura. Finite-time Lyapunov stability analysis and its application to atmospheric predictability, Journal of the Atmospheric Seciences. VoL50, Iss.11; p. 1531, (1993).
  • [2]. H, Komurcugil and 0, kukrer. Lyapunov-based control for three-phase PWM ACIDC voltage-source converters, IEEE Transactions on Power Electronics, Vo1.13, Iss.5; p.801, (1998).
  • [3]. Gen-Qi Xu and Siu Pang Yung. Lyapunov stability of abstract nonlinear dynamic system in Banach space, IMAjournal of mathematical control and information, Vol. 20, Iss 1, p. 105, (2003).
  • [4]. M. Yoshimasa. The Lyapunov stability of the N-soliton solutions in the Lax hieerarshy of the Benjamin- Ono equation, Journal of Mathematical Physics, VoL 47, Iss. 10; p. 1, (2006).
  • [5]. I, Karafyllis. Non-uniform robust global asymptotic stability for discrete-time systems and appliations to numerical analysis, IMA Journal of Mathematical Control and Information, Vol. 23, Iss. 1; p. 11, (2006).
  • [6]. C.H.Lee. solution Bounds of the Continuous and Discrete Lyapunov Matrix equations, Journal of Optimization Theory and applications, VoL 120, Iss.3; p. 559, (2004).
  • [7]. Shufang Xu and M Cheng. On the Solvability fort he mixed-type Lyapunov equation, IMA journal of Applied Mathematics, VoL71, Iss. 2; p. 287, (2006).
  • [8]. Richard C. H. Lee, C.W. Wong, Cheng-Zhong Xu, L.H.Yim and S.P. Yung. A Lyapunov-type condition for robust feedback stability of delay control systems, IMA journal of Mathematical control and Information, VoL 23, Iss. 1; p. 97, (2006).
  • [9]. E. Moulay and W. Perruquetti. Finite time stability of differential inclusions, IMA journal of Mathematical control and Information, Vol. 22, Iss. 4; p. 465, (2005).
  • [10]. Oliver Mason and Robert Shorten. On common quadratic Lyapunov functions for stable discretetime LTI systems, IMAjournal of Applied Mathematics, Vo1.69, Iss. 3; p. 271, (2004)
  • [11]. Elaydi saber, 1996, An Introduction to Difference Equations, springer, 31.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

A.Burcu Özyurt Serim This is me

Mustafa Bayram

Publication Date June 15, 2007
Published in Issue Year 2007 Issue: 013

Cite

APA Özyurt Serim, A., & Bayram, M. (2007). LYAPUNOV METODU iLE FARK DENKLEMLERiNiN KARARLILIGININ BELiRLENMESi. Journal of Science and Technology of Dumlupınar University(013), 31-38.

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