Analysis and synthesis of nonlinear systems having limit surfaces with prescribed stability properties

A method is presented for determining the dynamics of a system so that it will have prescribed hypersurfaces as limit sets with preassigned stability properties. This method is applicable not only to the synthesis of systems, but also to the analysis of nonlinear systems. This is equivalent to determining the approximate analytical solutions for multiple limit sets, or the boundary of the domain of attraction. Examples which verify this method are included.