TY - GEN
T1 - Malkin Lyapunov asymptotic stability of Caputo fractional-order time delay nonlinear system
AU - Li, Haoran
AU - Ren, Qifeng
AU - Kao, Yonggui
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - The idea of Malkin stability provides an important processing technique for the Lyapunov stability of the equilibrium point of the system. That is the first derivative of the Lyapunov function along the system trajectory is no longer required to be negative semi-definite, but the equilibrium point of the system can still be stable. In this paper, inspired by Malkin stability theorem of integer-order system, a Malkin stability theorem for Caputo fractional-order time delay nonlinear systems is given by using Razumikhin technique. Moreover, our result also guarantees the attractiveness of the equilibrium point of fractional-order time delay systems besides stability. Finally, the result of this paper is applied to Caputo fractional-order systems with both discrete and distributed delays, and the asymptotically stable criterion of the system equilibrium point is given by establishing an augmented Lyapunov functional.
AB - The idea of Malkin stability provides an important processing technique for the Lyapunov stability of the equilibrium point of the system. That is the first derivative of the Lyapunov function along the system trajectory is no longer required to be negative semi-definite, but the equilibrium point of the system can still be stable. In this paper, inspired by Malkin stability theorem of integer-order system, a Malkin stability theorem for Caputo fractional-order time delay nonlinear systems is given by using Razumikhin technique. Moreover, our result also guarantees the attractiveness of the equilibrium point of fractional-order time delay systems besides stability. Finally, the result of this paper is applied to Caputo fractional-order systems with both discrete and distributed delays, and the asymptotically stable criterion of the system equilibrium point is given by establishing an augmented Lyapunov functional.
KW - Caputo derivative
KW - Malkin stability
KW - asymptotically stable
KW - linear matrix inequality
KW - time-delay system
UR - https://www.scopus.com/pages/publications/85200332202
U2 - 10.1109/CCDC62350.2024.10587835
DO - 10.1109/CCDC62350.2024.10587835
M3 - 会议稿件
AN - SCOPUS:85200332202
T3 - Proceedings of the 36th Chinese Control and Decision Conference, CCDC 2024
SP - 1106
EP - 1111
BT - Proceedings of the 36th Chinese Control and Decision Conference, CCDC 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 36th Chinese Control and Decision Conference, CCDC 2024
Y2 - 25 May 2024 through 27 May 2024
ER -