Simplification of system model in time domain using continued fraction expansion in third Cauer form

An algorithm for determining the matrix continued fraction expansion in third Cauer form for a given state space model of a multivariable system directly, without the necessity for determining the corresponding transfer function matrix, is presented. This algorithm can be used for many applications such as determining the transfer function matrix from a state space model, system realisation, and simplification of a system model in the time domain. The procedure for simplification of a multivariable system model in the time domain has been outlined and an example has been given to illustrate the application.