- ▪M. L. J. Hautus, E.D. Sontag, "New results on pole-shifting for parametrized families of systems", J. Pure Appl. Algebra, vol. 40, no. 3, pp. 229–244, 1986. pdf
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.
- ▪R.T. Bumby, E.D. Sontag, H.J. Sussmann, W. Vasconcelos, "Remarks on the pole-shifting problem over rings", J. Pure Appl. Algebra, vol. 20, no. 2, pp. 113–127, 1981. pdf
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.