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Output feedback stabilization—Solution by algebraic geometry methods

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2 Author(s)
Anderson, B.D.O. ; University of Newcastle, New South Wales, Australia ; Scott, R.W.

Given an unstable finite-dimensional linear system, one can relate the existence of a memoryless feedback law stabilizing the system to the existence of a real solution of a set of multivariable polynomial inequalities. From these inequalities, a set of equalities may be constructed with two properties: the equality set has a real solution precisely when the inequality set does; generically the equality set has a finite number of solutions. Multivariable polynomial resultants provide a method of solving the equalities subject to the condition that the equalities have a finite number of solutions. The property that there is a finite number of solutions is established using some results of algebraic geometry.

Published in:

Proceedings of the IEEE  (Volume:65 ,  Issue: 6 )