Justification of the averaging method for a system of functional- differential equations with variable structure and impulses
The method of averaging is justified for a system of functional differential equations with variable structure (the right-hand side of the equation changes when the solution \(x: T\to {\mathbb{R}}^ n\) meets a given hypersurface \(f(t,x)=0\) in the extended state space \(T\times {\mathbb{R}}^ n)\), impulses (the solution ``jumps'' when meeting a hypersurface of the type \(t=t_ i(x))\) and a deviating argument depending on both x and t. The averaging scheme strongly simplifies the problem since it leads to an usual Cauchy problem for an ordinary differential equation in \({\mathbb{R}}^ n\).
functional differential equations with variable structure
scientific article; zbMATH DE number 4058010