An Alternative Discrete-Time Model for Networked Control Systems with time delay less than the sampling period

The majority of existing Networked Control Systems (NCS) models are discrete-time formulations based on the exact discretization of the continuous-time linear plant over a sample interval. In the state-space formalism, standard control textbooks suggest that a simple approach to model discrete-time LTI systems with time delay shorter or equal than the sampling period is to extend the state vector with a new state variable representing the last control signal, which implies increasing the order of the model by one. In this paper an alternative state-space model for discrete-time LTI systems with time delay is introduced that does not require increasing the order of the model. The relation between both the standard model and the new model is established, and the potential benefits of the new model with respect to the standard one are discussed. Numerical examples illustrate the concepts discussed throughout the paper.