Linear systems on partially ordered time sets

A point set with a partial order (poset) P is a useful "generalized time" set for linear system theory, since the fundamental concept of causality can be defined for linear operators on a function space on P. The causal-operator algebra has a rich structure, known to combinatorists. Specializing to posets which admit shift operators, some novel generalizations of time-invariance are obtained; P becomes an ordered semigroup. A Kalman-Wyman algebraic system theory is indicated for these systems.