Stability Analysis of a Linear Neutral Differential Equation

Yıl 2020, Cilt: 3 Sayı: 1, 29 - 32, 15.12.2020

Berrak Özgür

Öz

The main aim of this study is to give the stability analysis of linear neutral differential equations. As a special case, the third order linear neutral differential equation is considered and its characteristic equation is examined for the stability properties. The method used here is to analyze the roots of the third order characteristic equation by using the Sturm sequence. The given last theorem emphasizes the conditions obtained for getting positive real roots and also the importance of the system parameters for this situation.

Anahtar Kelimeler

Linear neutral differential equation, Stability analysis, Sturm sequence

Kaynakça

• 1 R. Bellman, K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963.
• 2 J. K. Hale, S. M. Verduyn Lunel, Introduction to functional differential equations, Springer, New York, 1993.
• 3 R. D. Driver, Ordinary and delay differential equations, Springer-Verlag, New York, 19677.
• 4 J. Forde, P. Nelson, Applications of Sturm sequences to bifurcation analysis of delay differential equation models, J. Math. Anal. Appl. 300(2) (2004), 273-284.
• 5 A. F. Yeniçerioğlu, C. Yazıcı, On the stability of third order linear autonomous neutral delay differential equations, Acad. J. Appl. Math. Sci. 3(3) (2017), 21-39.
• 6 B. Cahlon, D. Schmidt, Asymptotic stability of a mechanical robotics model with damping and delay, J. Math. Anal. Appl. 303 (2005), 36-53.
• 7 Z. Wang, J. Lam, K. J. Burnham Stability analysis and observer design for neutral delay systems, IEEE Trans. Automat. Contr. 47 (3) (2002), 478-483.
• 8 A. Bellen, N. Guglielmi, A. E. Ruehli Methods for linear systems of circuit delay differential equations of neutral type, IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46 (1999), 212-216.
• 9 Y. Kuang, Delay differential equations: with applications in population dynamics, Academic Press, San Diego, CA, USA, volume 191, 1993.