论文信息 - Linear Dynamical Systems over Integral Domains

Linear Dynamical Systems over Integral Domains

The notions of constant, discrete-time, and linear dynamical systems over a commutative ring and their corresponding input/output maps are defined and studied. Classical stability theory is generalized to systems over fields complete with respect to a rank-one valuation. The resulting ''p-adic stability theory'' is used to solve the realization problem for matrix sequences over a broad class of integral domains, generalizing results first announced in Rouchaleau, Wyman, and Kalman [Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 3404-3406].

Bostwick F. Wyman | Yves Rouchaleau | B. Wyman | Y. Rouchaleau

[1] P. Fatou. Séries trigonométriques et séries de Taylor , 1906 .

[2] N. Jacobson. Lectures In Abstract Algebra , 1951 .

[3] E. Polak,et al. System Theory , 1963 .

[4] G. David Forney,et al. Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

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

[6] W. Ledermann. Lectures in Abstract Algebra : vol. III, Theory of Fields and Galois Theory. By N. Jacobson. Pp. xi, 323. 76s. (Van Nostrand) , 1966 .

[7] Benali Benzaghou,et al. Algèbres de Hadamard , 1970 .

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

[9] Paul-Jean Cahen,et al. Éléments quasi-entiers et extensions de fatou , 1975 .

[10] 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.