Controllability and Observability of Multivariable Sampled Data Systems with Input and Output Delays

Abstract

Zero order hold discrete time equivalents of sampled data plants with multiple input and output delays are derived. The delay is not assumed to be an integral multiple of the sample period nor is it assumed identical for all inputs or outputs. It is proven that the discrete equivalent is both observable and controllable iff, (i) the discrete time equivalent with zero integral 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 useful design considerations when implementation delays are to be lumped with a discretized plant model.