Internal stabilization of stochastic 3D Navier–Stokes–Voigt equations with linearly multiplicative Gaussian noise

2019 ◽  
Vol 27 (3) ◽  
pp. 153-160
Author(s):  
Nguyen Van Thanh
Keyword(s):  
Gaussian Noise ◽  
Navier Stokes ◽  
Feedback Controllers ◽  
Internal Feedback ◽  
Internal Stabilization

Abstract We show that the 3D stochastic Navier–Stokes–Voigt equations with linearly multiplicative Gaussian noise can be stabilized in probability by linear internal feedback controllers with support large enough.

On Simple Design of Nonlinear Observers for Robust Stabilization of Nonlinear Systems

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Jacob Hammer
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Large Family ◽  
Feedback Controllers ◽  
Controlled System ◽  
Nonlinear Observers ◽  
Internal Stabilization ◽  
Strong Notion ◽  
Main Notion

Robust internal stabilization is a strong notion of stabilization, whereby stability is maintained regardless of small disturbances, noises, and uncertainties. In this paper, simple tools are developed for achieving robust internal stabilization of a rather large family of nonlinear systems. The main notion is that of a strict observer function, a function characterized by the following feature: subtracting a strict observer function from the differential equation of the controlled system results in an asymptotically stable differential equation. Strict observer functions are relatively easy to derive, and they directly yield robust asymptotic observers; the latter can be combined with robust state feedback controllers to achieve robust internal stabilization.

Sign in / Sign up

Export Citation Format

Share Document