Foundations of system theory: Decomposable systems

The algebraic language of category theory is the setting for a theory of reachability, observability and realization for a new class of systems, the decomposable systems, which generalize linear systems and group machines. Linearity is shown to play no role in the core results of Kalman's theory of linear systems. Moreover, we provide a new duality theory. The category-theoretic tools of powers, copowers and image factorization provide the foundations for this study. Even though the results are more general, the proofs are simpler than those of the classical linear theory, once the basic category theory, presented here as a self-contained exposition, has been mastered.