Regular Papers

International Journal of Control, Automation and Systems 2018; 16(4): 1532-1540

Published online May 15, 2018

https://doi.org/10.1007/s12555-017-0354-1

© The International Journal of Control, Automation, and Systems

Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay

Xuegang Tan, Bin Hu, Zhi-Hong Guan*, Rui-Quan Liao, Jiang-Wen Xiao, and Yuehua Huang

Huazhong University of Science and Technology

Abstract

This paper investigates a model of hybrid impulsive and switching stochastic systems (HISSS) with time-delay. Several stability criteria, including the globally asymptotical and exponential stability criteria in the pth moment and mean square, are established by using Itô formula, a generalized switching Lyapunov functions and some relating techniques. Especially, a more general Lyapunov-Krasivskii functional is constructed, and it is observed that the mean square asymptotic and exponential stability conditions of HISSS are delay-dependent. A numerical example shows that the obtained stability results can reduce the conservativeness."

Keywords Hybrid stochastic differential systems, impulsive and switching, stability, time delay.

Article

Regular Papers

International Journal of Control, Automation and Systems 2018; 16(4): 1532-1540

Published online August 1, 2018 https://doi.org/10.1007/s12555-017-0354-1

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

Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay

Xuegang Tan, Bin Hu, Zhi-Hong Guan*, Rui-Quan Liao, Jiang-Wen Xiao, and Yuehua Huang

Huazhong University of Science and Technology

Abstract

This paper investigates a model of hybrid impulsive and switching stochastic systems (HISSS) with time-delay. Several stability criteria, including the globally asymptotical and exponential stability criteria in the pth moment and mean square, are established by using Itô formula, a generalized switching Lyapunov functions and some relating techniques. Especially, a more general Lyapunov-Krasivskii functional is constructed, and it is observed that the mean square asymptotic and exponential stability conditions of HISSS are delay-dependent. A numerical example shows that the obtained stability results can reduce the conservativeness."

Keywords: Hybrid stochastic differential systems, impulsive and switching, stability, time delay.

IJCAS
July 2024

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

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