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. It reveals to be very useful to study the impact of Finite Word Length implementation, especially in the case of embedded controller. Numerous works concerned the design of the ”best” realization concerning parameterisation, numerical noise minimisation or saving computation. 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 computations to be performed. It is necessary to describe some popular algorithms simulating LTI systems. Moreover, such a representation has the important property to unify different ways of research considering differently the possibilities offered by using the shift, δ or γ operators. Copyright c ©2005 IFAC