1. M. L. J. Hautus and E.D. Sontag. New results on pole-shifting for parametrized families of systems. J. Pure Appl. Algebra, 40(3):229-244, 1986. [PDF] Keyword(s): systems over rings, pole-shifting, parametric classes of systems, real-analytic functions. Abstract:

   New results are given on the pole-shifting problem for commutative rings, and these are then applied to conclude that rings of continuous, smooth, or real-analytic functions on a manifold X are PA rings if and only if X is one-dimensional.




2. R.T. Bumby, E.D. Sontag, H.J. Sussmann, and W. Vasconcelos. Remarks on the pole-shifting problem over rings. J. Pure Appl. Algebra, 20(2):113-127, 1981. [PDF] Keyword(s): systems over rings, systems over rings. Abstract:

   Problems that appear in trying to extend linear control results to systems over rings R have attracted considerable attention lately. This interest has been due mainly to applications-oriented motivations (in particular, dealing with delay-differential equations), and partly to a purely algebraic interest. Given a square n-matrix F and an n-row matrix G. pole-shifting problems consist in obtaining more or less arbitrary characteristic polynomials for F+GK, for suitable ("feedback") matrices K. A review of known facts is given, various partial results are proved, and the case n=2 is studied in some detail.

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