Output Feedback Stabilization—Solution by Algebraic Geometry Methods

Brian D.O. Anderson; Raymond W. Scott

doi:10.1109/PROC.1977.10581

Output Feedback Stabilization—Solution by Algebraic Geometry Methods

Brian D.O. Anderson, Raymond W. Scott

Research output: Contribution to journal › Article › peer-review

44 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	849-861
Number of pages	13
Journal	Proceedings of the IEEE
Volume	65
Issue number	6
DOIs	https://doi.org/10.1109/PROC.1977.10581
Publication status	Published - Jun 1977
Externally published	Yes

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Output Feedback Stabilization—Solution by Algebraic Geometry Methods

Abstract

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