Extended state-space model of discrete-time dynamical systems

A model for discrete-time dynamical systems is discussed in which the future values of the internal variables depend on the present and K - 1 previous time instants, where K is the order of the model. We outline transition matrix and impulse response calculations, equivalences between model and conventional state variable models, methods of constructing such a model, and means for calculating certain quantities relevant to the design of cost-optimal low-roundoff noise digital filters.