Linear dynamical systems over integral domains

  • Authors:

  • Yves Rouchaleau;Bostwick F. Wyman

  • Affiliations:

  • -;Stanford University, Palo Alto, California 94305, USA and Ohio State University, Columbus, Ohio 43210, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1974

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Abstract

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].