A transfer function representation for a class of hyperbolic systems

Results of the transfer function analysis for a class of distributed parameter systems described by hyperbolic partial differential equations are presented. Assuming two lumped boundary inputs and two outputs distributed along the spatial variable, the expressions for the individual elements of the transfer function matrix are derived for the decoupled system, using both exponential and hyperbolic functions. A formula for converting the transfer function matrix to the form describing the original coupled system is also proposed. The considerations are illustrated with a practical example of an electrical transmission line.