Equivalent higher order linear and non-linear systems

The object of this study is to put forth the concept of equivalence of classes of linear and non-linear systems of higher order. In particular, the equivalence of classes of non-linear (non-autonomous/autonomous) systems of order n described by partial/ordinary differential equations with corresponding classes of linear systems of order (n + 1) is established through a differential transformation of the dependent variable. In view of the fact that the resulting linear systems are amenable to existing state-space techniques, this approach can be expected to be of value in the study of many non-linear problems arising in a variety of disciplines. The possible applications of the technique are illustrated with an example.