Generalized zero sets of multiparameter polynomials and feedback stabilization

Author

Walach, Eugene ; Zeheb, Ezra

Volume

29

Issue

1

fYear

1982

fDate

1/1/1982 12:00:00 AM

Firstpage

15

Lastpage

23

Abstract

A new theorem is stated and proved, which enables one to find the set of points $z$ in the closed complex plane such that for every $m$ -dimensional vector of parameters $u^{0}\\in Q$ , there exists an $n$ -dimensional vector of parameters $\\upsilon ^{0} \\in P$ rendering $F( \\upsilon ^{0}, u^{0}, z ) = 0$ , where $F$ is a given polynomial in $z$ depending analytically and continuously on two sets of parameters $\\upsilon$ and $u$ , and $Q$ and $P$ are the Cartesian products of the given domains of definition of each of the parameters $u_{i}$ and $\\upsilon _{i}$ , respectively. A numerical example is provided. The new theorem is used to answer the question whether there exists a feedback matrix, with possible constraints on its entries, which stabilizes a linear system with any number of inputs and outputs. If such a matrix exists, a procedure is outlined to find one. A numerical example is provided, which shows that this new method is computationally simpler than previous procedures.

Keywords

General circuits and systems theory; Output feedback, linear systems; Polynomials; Stability, linear systems; Circuits and systems; Constraint theory; Functional analysis; Linear systems; Output feedback; Polynomials; State feedback;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1982.1085080

Filename

1085080