Discrete-Time Systems with the Decomposition Property

The decomposition property, a necessary condition for linearity, is defined for discrete-time systems. N-state machines with this property have finite memory μ≤N−1. Linear and autonomous systems are important classes of systems with decomposition. Several representations of systems with decomposition are given and a general form of the discrete-time state equations for a finite-memory system with decomposition is derived. An algorithm is developed by which an arbitrary complete-sequential machine may be tested for decomposition.