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Sun et al. Complex Eng Syst 2022;2:17 Complex Engineering
DOI: 10.20517/ces.2022.48 Systems

Research Article Open Access

Stability analysis for highly nonlinear switched stochas-

tic systems with time-varying delays

1
Jing Sun , Hui Wang 1,2,3
1 School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China.
2 Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044,
Jiangsu, China.
3 Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and
Technology, Nanjing 210044, Jiangsu, China.

Correspondence to: Dr. Hui Wang, School of Mathematics and Statistics, Nanjing University of Information Science and Technol-
ogy, No. 219 Ningliu Road, Nanjing 210044, Jiangsu, China. E-mail: wang_8063085@163.com
How to cite this article: Sun J, Wang H. Stability analysis for highly nonlinear switched stochastic systems with time-varying delays.
Complex Eng Syst 2022;2:17. http://dx.doi.org/10.20517/ces.2022.48
Received: 11 Nov 2022 First Decision: 30 Nov 2022 Revised: 19 Dec 2022 Accepted: 21 Dec 2022 Published: 27 Dec
2022
Academic Editor: Hamid Reza Karimi Copy Editor: Fanglin Lan Production Editor: Fanglin Lan

Abstract
In this paper, we examine the stability of highly nonlinear switched stochastic systems (SSSs) with time-varying de-
lays, where the switching time instants are deterministic rather than stochastic. Herein, the boundedness of the
global solution is first proven for highly nonlinear SSSs via the average dwell time (ADT) method and multiple Lya-
punov function (MLF) approach. Then, the stability criteria for th moment exponential stability and almost surely
exponential stability are presented. The main difficulty lies in the presence of switching and time-varying delay terms,
which prevents the validation of existing methods. New inequality techniques have been developed to counteract the
effects of switching signals and time-varying delays. Finally, an example is provided to verify the effectiveness of the
results.

Keywords: Highly nonlinear switched stochastic systems, deterministic switching signal, time-varying delays, aver-
age dwell time, multiple Lyapunov function

© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0
International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, shar-
ing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you
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