Feedback linearisation of nonlinear vibration problems: A new formulation by the method of receptances

•New formulation for output feedback linearisation.•New zero-dynamics theory.•No need to know or evaluate the system matrices.•No need to know the functional form or parameters of the nonlinearity.•Method of receptances.

New output feedback-linearisation theory is presented for the treatment of nonlinear vibration problems by a receptance-based approach. An important aspect is a new formulation for investigating the stability of the zero dynamics. The overall methodology possesses the usual benefits of the receptance method, namely that the system matrices (with associated assumptions and approximations) do not have to be known. In addition, it has the distinction of not requiring the form and parameter values of the nonlinearity when the input and output degrees of freedom are away from the nonlinearity itself. This represents a valuable advance over the conventional time-domain feedback linearisation approach.