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This research focuses on the stochastic functional differential equations driven by G-Brownian motion (G-SFDEs) with infinite delay. It is proved that the trivial solution of a G-SFDE with infinite delay is exponentially stable in mean square. An example is also presented to illustrate the effectiveness of the obtained theory.

In order to determine the recommended flow velocity for the safe and energy-saving transport of ice-slurry-type light particle slurries, it is necessary to study the flow characteristics of light particle slurries, especially the critical flow velocity. Therefore, in this paper, a numerical simulation method based on the mixed turbulence model with the RANS (Reynolds averaged Navier Stokes) equation is used, and a new concentration distribution method is proposed for the first time to derive the critical flow velocity, as follows: the flow velocity of the light particle slurry when the ratio of the solid volume fraction vf at the position of 0.08D above the bottom of the pipeline to that at the center of the pipeline, vf/vf(y) = 0.75, is taken as the critical flow velocity. The flow changes in the slurry (polyethylene particles with a density of 922 kg/m3 and water) under 0.1–1.0 m/s (at intervals of 0.1 m/s) were investigated experimentally, and the pressure drop data obtained from the experiments were used to determine the recommended flow rate for safe and energy-saving transportation of the light particle slurry. The pipe diameter used for the experiments and simulations was 28 mm, and the solid-phase particle sizes were 0.3 mm, 0.4 mm, and 0.5 mm, with solid-phase contents of 5 vol%, 10 vol%, 15 vol%, and 20 vol%. In addition, the experimental and numerical simulation results show that an increase in solid-phase content and particle size leads to an increase in critical flow velocity. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]