Stabilisation of stochastic multi-group models driven by G-Brownian motion via delay feedback control

Abstract

ABSTRACT For the potential applications in uncertainty problems, risk measures and superhedging problems in finance, the theory of nonlinear expectation attracts researchers’ great interest. Base on G-expectation, in this work, we discuss the stabilisation issue for a class of stochastic multi-group models driven by G-Brownian motion (G-MGMs, in short) via delay feedback control design. By employing the concept of graph theory and G-Lyapunov approach, we establish both Lyapunov criteria and coefficient-type criteria for guaranteeing the stabilisation of the addressed model. Further, a class of stochastic coupled oscillators driven by G-Brownian motion is discussed. Finally, an example is offered to verify the validity of the obtained theoretical results.