Two classes of efficient digital controller structures with stability consideration

In this note, the efficient controller structure problem is investigated subject to minimizing finite word length (FWL) effects. Two classes of sparse controller structures characterized with a set of free parameters are derived. The stability behavior of each class is analyzed with a newly defined stability related measure. The optimal structure problems are studied in terms of maximizing the stability related measure for the two classes of sparse structures as well as the fully parametrized state-space realizations. A design example is given, which shows that the optimized sparse structures can beat the fully parametrized optimal realizations in terms of both stability performance and computation efficiency.