Feedback linearisation of time-varying nonlinear systems via time-varying diffeomorphism

A control scheme is proposed to stabilise a class of time-varying nonlinear systems. The scheme is based on the feedback-linearisation scheme and is developed via the newly proposed time-varying diffeomorphism concept, which results in the transformation of time-varying systems into equivalent time-invariant linear systems. As a result, feedback linearisation of time-varying nonlinear systems is achieved and it provides the stabilisation of a class of nonlinear time-varying systems. In addition, the approximate feedback LTIsation concept is introduced for its practicability.