Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting monotone with p-growth. This work dedicated a quantitative two-scale expansion result. By treating range exponents $$2\le p <\infty $$ in dimensions $$d\le 3$$ , are able consider genuinely equations and systems such as $$-\nabla \cdot A(x)...

This paper presents a general approach to design a partially stabilizing controller for nonlinear systems. In this approach, the nonlinear control system is divided into two subsystems, which are called the first and the second subsystems. This division is done based on the required stability properties of system’s states. Furthermore, it is shown that partial control makes the possibility of c...