Averaging of systems of differential inclusions with slow and fast variables (Q946120)

The aim of this paper is to present an averaging principle for the following class of one-sided Lipschitz systems of differential inclusions \[ \dot{x} \in \mu F(t,x,y,\mu), x(0)=x_0, \dot{y} \in G(t,x,y,\mu), y(0)=y_0; \] where \(F\) and \(G\) are multivalued mappings with convex compact values in \(\mathbb{R}^{m_1}\) and \(\mathbb{R}^{m_2}\) respectively. Under suitable assumptions, it is shown that the averaged problem \[ \dot{u} \in \mu F_0(u), u(0)=x_0, \] is a mutual approximation to the above system.