On a certain class of nonlinear control systems

Nonlinear systems of the following type (I):
\dot{x}_{i} = \Sigma\min{j=1}\max{n} (a_{ij} + k\dotb_{ij})\dotx_{j} + \Sigma\min{j=1}\max{p} d_{ij}\dotu_{j} + \Sigma\min{j,k=1}\max{n} n_{ijk}\dotx_{j}\dotx_{k} + \Sigma\min{j,k,l=1} m_{ijkl}\dotx_{j}\dotx_{k}\dotx_{l} (k\inR^{1},k
feedback factor,
i = 1,...,n
) have recently been investigated from the point of view of practical stability [1]. This note shows how to model type (I) systems as feedback systems consisting of "general quadratic and cubic" plants and controllers. Certain nonanalytic nonlinear systems can approximately be treated within the framework of this model.