Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

Abstract

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Keywords

• mean-square stability
• stochastic system
• G-Brownian motion
• Lyapunov–Krasovskii function
• linear matrix inequality (LMI)