Minimal realisation of the transfer function matrix with multiple time delays

A minimal realisation scheme for a class of multiple time-delay transfer function matrices with distinct poles is presented. Also, a simple minimal realisation method is developed for a specific two-input-two-output multiple time-delay system whose poles can be repeated. In addition, a state-space discretisation technique developed for a multivariable system with a single time delay is extended to a multivariable system with multiple time delays. Finally, it should be mentioned that the proposed approach is restricted to systems where multiple time delays arise only in the input and output, and not in the state. Illustrative examples are given to demonstrate the effectiveness of the proposed method.