Constructing sparse realisations of finite-precision digital controllers based on a closed-loop stability related measure

The authors present a study of the finite word length (FWL) implementation for digital controller structures with sparseness consideration. A closed-loop stability related measure is derived, taking into account the number of trivial elements in a controller realisation. A practical design procedure is presented, which first obtains a controller realisation that maximises a lower bound of the proposed measure, and then uses a stepwise algorithm to make the realisation sparse. Simulation results show that the proposed design procedure yields computationally efficient controller realisations with an enhanced FWL closed-loop stability performance.