Practical stability in relation to a part of variables for stochastic reaction-diffusion systems driven by G-Brownian motion

Article Automation & Control Systems

Delay feedback stabilisation of stochastic differential equations driven by G-Brownian motion

Yuyuan Li et al.

Summary: This paper proposes a method to design feedback control to stabilize a class of nonlinear stochastic differential equations, ensuring exponential stability of the system. It provides methods for determining the length of the time delay and designing the delay feedback controller, and demonstrates the theory with a numerical example.

INTERNATIONAL JOURNAL OF CONTROL (2022)

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Article Mathematics, Applied

Practical stability with respect to a part of variables of stochastic differential equations

Tomas Caraballo et al.

Summary: This paper studies the practical stability of nonlinear stochastic differential equations with respect to some variables. The analysis includes global practical uniform asymptotic stability, global practical uniform pth moment exponential stability, and global practical uniform exponential stability using Lyapunov techniques. Illustrative examples are provided to demonstrate the usefulness of this notion of stability with respect to a part of the variables.

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES (2021)

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Article Mathematics, Applied