Stability analysis of switched stochastic nonlinear systems with state-dependent delay

• Published in: IEEE transactions on automatic control Vol. 69; no. 4; pp. 1 - 8
• Main Authors: Fan, Lina, Zhu, Quanxin, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control theory; Delay; Delays; Hybrid systems; multiple Lyapunov-Krasovskii functional; Nonlinear systems; Random variables; Stability; Stability analysis; State-dependent delay; Stochastic systems; stochastically weakly locally exponential stability; switched stochastic system; Switched systems; Switches
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3315672

This paper is devoted to solving the problem of stochastically weakly locally exponential stability of switched stochastic systems with state-dependent delay. Different from the previous works, we introduce the state-dependent delay, which is a random variable dependent on the system state so that the bound of the delay is unknown. In addition, we also consider the influence of switching on the stability of the system. By using multiple Lyapunov-Krasovskii functionals and some novel stochastic analysis techniques, we obtain sufficient conditions for stochastically weakly locally exponential stability of the hybrid system. Two examples are provided to verify the correctness of the proposed results.