Towards the Computation of Stabilizing Controllers of Multidimensional Systems
Résumé
In this paper, we further study the effective computation of stabilizing controllers of multidimensional systems. Within the algebraic analysis approach, the stabilization problem can be characterized by the fact that a certain finitely presented A-module M, naturally associated with the multidimensional system, is projective, where A denotes the ring of multivariate rational functions without poles in the closed complex unit polydisc D^n . This condition can be reduced to the existence of an element s of a polynomial ideal I which has no zero in D^n .
According to the Polydisc Nullstellensatz, the latter condition is equivalent to the fact that no complex zero of the elements of I belongs to D^n . If this condition is satisfied, using cyclic resultants and linear programming, we then propose a method to compute such a polynomial s.
Finally, using computer algebra methods for effectively handling basic operations on R[s^(-1) ]modules, where R is a polynomial ring, we show how to compute stabilizing controllers.
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