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An introduction to the stabilization problem for parametrized families of linear systems. (English) Zbl 0581.93051
Linear algebra and its role in systems theory, Proc. AMS-IMS-SIAM Conf., Brunswick/Maine 1984, Contemp. Math. 47, 369-400 (1985).

[For the entire collection see Zbl 0568.00005.]

The paper represents a concise coverage of the most significant known facts about the stabilization of parametrized families of linear systems. Several fundamental theorems with respect to pole-assignability using static and dynamic controllers are reviewed in the first part.

The following two sectins deal with stabilization problems for controllable and asycontrollable families, the special cases of ring controllability respectively of ring-asycontrollability being fully developped.

The work ends with the demonstration of a new result: the pointwise asycontrollable continuous-time polynomial of rational families, and discrete-time ratinal families are asycontrollable and can be dynamically stabilized.

Reviewer: O.Pastravanu
MSC:
93D15Stabilization of systems by feedback
93B35Sensitivity (robustness) of control systems
93C05Linear control systems
93B05Controllability
93B25Algebraic theory of control systems