Asymptotic stability of dynamical systems with Barbalat’s lemma and Lyapunov function

216 views

Authors

DOI:

https://doi.org/10.54939/1859-1043.j.mst.CSCE6.2022.122-130

Keywords:

Lemma Barbalat; Lyapunov function; Theorem Lagrange; Asymptotic stability; Non-autonomous system.

Abstract

The article explains Barbalat’s lemma, combining the application of Barbalat’s lemma, the Lyapunov function, and the theorem Lagrange to ensure mathematical certainty in analyzing the asymptotic stability of a non-autonomous control system. Research results are illustrated and simulated with visual examples of uncontrolled and controlled dynamical systems.

References

[1]. Hung JY, Gao W, Hung JC, “Variable Structure Control: A Survey”, IEEE Transaction on Industrial Electronics, Vol. 40, No. 1, pp. 2-22, (1993). DOI: https://doi.org/10.1109/41.184817

[2]. Ying-Ying M., L. Yun-Gang, “Barbalat lemma and its application in analysis of system stability”, Journal of Shandong University (Engineering Science), 37(1), 51–56, (2007).

[3]. Slotine and Li, “Applied nonlinear control”, Prentice Hall, pp. 125, (1991).

[4]. Khalil, H. K., “Nonlinear systems”, Englewood Cliffs, NJ: Prentice Hall, (1996).

[5]. Hou, M., Duan, G., & Guo, M., “New versions of Barbalat’s lemma with applications”, Journal of Control Theory, (2010). DOI: https://doi.org/10.1007/s11768-010-8178-z

[6]. Narendra, K. S., & Annaswamy, M., “Stable adaptive systems”, New York, NY: Dover Publications Inc, (2005).

[7]. Yu, X., & Wu, Z., “Corrections to Stochastic Barbalats lemma and its applications”, IEEE Transactions on Automatic Control, 59, 1386–1390, (2014). DOI: https://doi.org/10.1109/TAC.2013.2283752

[8]. Nguyễn Ngọc Cư, Lê Huy Đạm, Trịnh Danh Đằng, Trần Thanh Sơn, “Giải tích 1”, Nhà xuất bản ĐHQG, Hà Nội, (2004).

[9]. Nguyen Thi Thu Thao, Vu Quoc Huy, “Sliding mode control with exponent sliding surface-reaching law in the tracking drive systems using synchronous servo at torque-position mode”, Journal of Military Science and Technology, No. 80, pp. 31-38, (2022).

Downloads

Published

30-12-2022

How to Cite

Vu Quoc, D. H. “Asymptotic Stability of Dynamical Systems With Barbalat’s Lemma and Lyapunov Function”. Journal of Military Science and Technology, no. CSCE6, Dec. 2022, pp. 122-30, doi:10.54939/1859-1043.j.mst.CSCE6.2022.122-130.

Issue

Section

Research Articles

Categories