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New results in subspace-stabilization control theory. (English) Zbl 1002.49027

Summary: Subspace-stabilization is a generalization of the classical idea of stabilizing motions of a dynamical system to an equilibrium state. The concept of subspace-stabilization and a theory for designing subspace-stabilizing control laws was introduced in a previously published paper. In the present paper, two new alternative methods for designing control laws that achieve subspace-stabilization are presented. These two alternative design methods are based on: (i) a novel application of existing linear-quadratic regulator optimal control theory, and (ii) an algebraic method in which the control-law is expressed as a linear feedback of certain “canonical variables.” In some cases, these new design methods may be more effective than existing ones. The results are illustrated by worked examples.

MSC:

49N10 Linear-quadratic optimal control problems
93D15 Stabilization of systems by feedback
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