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Routh stability criterion and Lyapunov-Routh method in control theory | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 15، شماره 5، مرداد 2024، صفحه 111-120 اصل مقاله (512.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.31372.4570 | ||
| نویسندگان | ||
| Ali Farhan Hashosh1؛ Hadi Basirzadeh* 2 | ||
| 1Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran | ||
| تاریخ دریافت: 25 بهمن 1401، تاریخ بازنگری: 20 فروردین 1402، تاریخ پذیرش: 11 تیر 1402 | ||
| چکیده | ||
| One of the most important issues in the linear control subject is to obtain eigenvalues of the system to study the stability of a system. It is needed to identify the sign of eigenvalues but not the value of it. To fulfil this, there are different methods such as Routh stability criterion, Lyapunov’s method and Nyquist stability criterion. In this research, we will present the most simple one to determine the sign of eigenvalues and we shall discuss and explain different types of stability. Also, we will discuss some special cases that cross a controversial mission, and a new method is proposed to calculate the stability of systems, which we call the Lyapunov-Routh method (composition of Lyapunov and Routh method). | ||
| کلیدواژهها | ||
| Stability؛ Stability types؛ Routh-Hurwitz stability criterion؛ Lyapunov’s method | ||
| مراجع | ||
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[1] V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, Open Problems in Mathematical Systems and Control Theory, Springer Science & Business Media, 2012. [2] D.N. Burghes and A. Graham, Control and optimal control theories with applications, Horwood Publishing, 2004. [3] K. Dekker, Formula manipulation in ALGOL 68 and application to Routh’s algorithm, Computing 26 (1981), 167–187. [4] F. Golnaraghi and B.C. Kuo, Automatic Control Systems. McGraw-Hill Education, 2017. [5] M. Gopal, Control Systems Principles and Design, Second edition, Tata McGraw Hill, 2000. [6] G. Leitmann, The Calculus of Variations and Optimal Control: An Introduction, Springer Science & Business Media, 2013. [7] A.P. Liyaw, Hgram patterns of Routh Stability zones in linear systems, Int. J. Math. Educ. Sci. Technol. 28 (1997), no. 2, 225–241. [8] J. Macki and A. Strauss, Introduction to Optimal Control Theory, Springer Science & Business Media, 2012. [9] T.D. Roopamala and S.K. Katti, Comments on Routh stability criterion, Int. J. Comput. Sci. Inf. Secur. 7 (2010), 77–78. [10] E.J. Routh, A Treatise on the Stability of Motion, Macmillan, London, U. K., 1877. [11] Q. Li, What can Routh table offer in addition to stability?, J. Control Theory Appl. 1 (2003), no. 1, 9–16. | ||
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