On Split Realizations of Response Maps over Rings

This paper deals with observability properties of realizations of linear response maps defined over commutative rings. A characterization is given for those maps which admit realizations which are simultaneously reachable and observable in a strong sense. Applications are given to delay-differential systems.

[1]  W. Wonham,et al.  Topics in mathematical system theory , 1972, IEEE Transactions on Automatic Control.

[2]  W. Ching,et al.  Linear discrete time systems over commutative rings , 1976 .

[3]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[4]  Eduardo Sontag.  Linear Systems over Commutative Rings. A Survey , 1976 .

[5]  Eduardo D. Sontag,et al.  On the Existence of Minimal Realizations of Linear Dynamical Systems over Noetherian Integral Domains , 1979, J. Comput. Syst. Sci..

[6]  R. Tennant.  Algebra , 1941, Nature.

[7]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[8]  R E Kalman,et al.  Algebraic Structure of Linear Dynamical Systems. III. Realization Theory Over a Commutative Ring. , 1972, Proceedings of the National Academy of Sciences of the United States of America.