Implicit State-Space Representation : a Unifying Framework for FWL Implementation of LTI Systems

Practically, some intermediary realizations are used in order to simulate numerically dynamic systems. One of the most popular is the state-space realization that is very useful to study the impact of Finite Word Length implementation, specially on embedded controller.Numerous works concerned the design of the "best" realization concerning parameterization, numerical noise minimisation. This paper points out however that a standard state-space realization is too basic to take into account some interesting realizations. On the contrary, it highlights that implicit state-space realizations allows a more direct link with the macroscopic computation to be performed. It is necessary to describe some popular algorithms simulating LTI systems and has the important property to unify different ways of research considering the possibilities offered by using the shift, delta or gamma operators.