Discrete Equivalent of Multivariable Plants with Input and Output Delays

The zero order hold discrete time equivalent of a multivariable plant with delays in the input and output is derived. It is proven that the discrete equivalent is both observable and controllable if, (i) the discrete time equivalent with zero delay is both observable and controllable, (ii) the number of plant inputs and outputs is equal and (iii) there are no transmission zeros at the origin. These are important considerations when embarking on a digital control system design in which implementation delays are to be included with the discrete plant model.