Stochastic Intermittent Control with Uncertainty

Zhengqi Ma, Hongyin Jiang, Chun Li, Defei Zhang () and Xiaoyou Liu
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Zhengqi Ma: School of Mathematics and Statistic, Honghe University, Mengzi 661100, China
Hongyin Jiang: School of Mathematics and Statistic, Puer University, Puer 665000, China
Chun Li: School of Mathematics and Statistic, Honghe University, Mengzi 661100, China
Defei Zhang: School of Mathematics and Statistic, Honghe University, Mengzi 661100, China
Xiaoyou Liu: School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China

Mathematics, 2024, vol. 12, issue 13, 1-15

Abstract: In this article, we delve into the exponential stability of uncertainty systems characterized by stochastic differential equations driven by G-Brownian motion, where coefficient uncertainty exists. To stabilize the system when it is unstable, we consider incorporating a delayed stochastic term. By employing linear matrix inequalities (LMI) and Lyapunov–Krasovskii functions, we derive a sufficient condition for stabilization. Our findings demonstrate that an unstable system can be stabilized with a control interval within ( θ * , 1 ) . Some numerical examples are provided at the end to validate the correctness of our theoretical results.

Keywords: coefficient uncertainty; lyapunov-krasovskii function; LMI (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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