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On the stabilization of the homogeneous bilinear systems. (English) Zbl 0794.93089
Summary: The problem of stabilizing the single-input homogeneous bilinear systems is considered. A special class of these systems is considered: the matrix of the linear (i.e., control independent) term of the right-hand side is semistable while the matrix of the bilinear term is skew-symmetric. Two types of stabilization are investigated: constant feedback global asymptotic stabilization and practical stabilization by a family of the linear feedbacks. It is shown for the planar case that the above system is always practically stabilizable by a family of the linear feedbacks. For \(n=3\), the solution of both stabilization problems depends on the mutual position of the expanding direction of the linear part and the direction of the infinitesimal rotation defined by the bilinear term.

MSC:
93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
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