Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(5): 1537-1544

https://doi.org/10.1007/s12555-022-1233-y

© The International Journal of Control, Automation, and Systems

The Relationship Between Augmented Lyapunov-Krasovskii Functionals and Estimated Inequalities

Daixi Liao*, Shouming Zhong, Jun Cheng, Kaibo Shi, Shaohua Long, and Can Zhao

Hunan Institute of Technology

Abstract

Different estimated inequalities and augmented Lyapunov-Krasovskii functionals (LKFs) play important role in assessing the stability of time-delay systems. In this technical note, three categories of estimated inequalities are introduced, in which either all matrices, some matrices or no matrices are free. Then, the internal relationship among the three categories of estimated inequalities is fully revealed. Next, an optimal method is provided for selecting the estimated inequalities and constructing the Lyapunov-Krasovskii functionals. That is, the inequalities and the functionals should tailor for each other (see Table 2), which is proved theoretically. Finally, a numerical example is presented to verify the results.

Keywords Estimated inequalities, Lyapunov-Krasovskii functionals, stability, time delay.

Article

Regular Papers

International Journal of Control, Automation, and Systems 2024; 22(5): 1537-1544

Published online May 1, 2024 https://doi.org/10.1007/s12555-022-1233-y

Copyright © The International Journal of Control, Automation, and Systems.

The Relationship Between Augmented Lyapunov-Krasovskii Functionals and Estimated Inequalities

Daixi Liao*, Shouming Zhong, Jun Cheng, Kaibo Shi, Shaohua Long, and Can Zhao

Hunan Institute of Technology

Abstract

Different estimated inequalities and augmented Lyapunov-Krasovskii functionals (LKFs) play important role in assessing the stability of time-delay systems. In this technical note, three categories of estimated inequalities are introduced, in which either all matrices, some matrices or no matrices are free. Then, the internal relationship among the three categories of estimated inequalities is fully revealed. Next, an optimal method is provided for selecting the estimated inequalities and constructing the Lyapunov-Krasovskii functionals. That is, the inequalities and the functionals should tailor for each other (see Table 2), which is proved theoretically. Finally, a numerical example is presented to verify the results.

Keywords: Estimated inequalities, Lyapunov-Krasovskii functionals, stability, time delay.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

Stats or Metrics

Share this article on

  • line

Related articles in IJCAS

IJCAS

eISSN 2005-4092
pISSN 1598-6446