MINIMALITY AND OBSERVABILITY OF GROUP SYSTEMS

Group systems are a generalization of Willems-type linear systems that are useful in error control coding. It is shown that the basic ideas of Willems's treatment of linear systems are easily generalized to lin ear systems over arbitrary rings and to group systems. The interplay b etween systems (behaviors) and trellises (evolution laws) is discussed with respect to completeness, minimality, controllability, and observ ability. It is pointed out that, for trellises of group systems and Wi llems-type linear systems, minimality is essentially the same as obser vability. The development is universal-algebraic in nature and holds u nconditionally for linear systems over the real numbers.