A unified minimal realization theory with duality
A unified minimal realization theory with duality
Coproducts and decomposable machines
Journal of Computer and System Sciences
On the relevance of abstract algebra to control theory
Automatica (Journal of IFAC)
An algebraic model of synchronous systems
Information and Computation
Paper: Geometric state-space theory in linear multivariable control: A status report
Automatica (Journal of IFAC)
The duality of state and observation in probabilistic transition systems
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
Geometrically minimal realizations of Boolean controlled systems
Automation and Remote Control
| Hi-index | 22.15 |
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.