A graphical test for checking the stability of a linear time-invariant feedback system

Author

Callier, Frank M. ; Desoer, Charles A.

Author_Institution

University of California, Berkeley, CA, USA and Belgian National Fund for Scientific Research, Brussels, Belgium

Volume

Issue

fYear

1972

fDate

12/1/1972 12:00:00 AM

Firstpage

773

Lastpage

780

Abstract

A graphical test is developed for checking the condition $\\inf_{\\Re s \\geq 0}|1 + k\\hat{g}(s)| > 0$ where $k$ is a nonzero real constant and $\\hat{g}$ is the sum of a finite number of right-half plane poles and the Laplace transform of an integrable function plus a series of delayed impulses. As a conseqence, $1 + k\\hat{g}$ is, in $\\Re s \\geq 0$ , asymptotic to an almost periodic function, say $\\hat{f}$ , for $|s| \\rightarrow \\infty$ . Theorem 1 gives a necessary and sufficient condition involving the curve ${\\hat{f}(j\\omega )|\\omega \\in R}$ to ensure that $\\inf_{\\Re s \\geq 0} |\\hat{f}(s)| > 0$ ; Corollary 1 gives a corresponding graphical test. Theorem 2 and Corollary 2 give a necessary and sufficient condition involving the curve ${1 + K\\hat{g}(j\\omega )|\\omega \\in R}$ and a graphical test to ensure $\\inf_{\\Re s \\geq 0}| + k\\hat{g}(s)| > 0$ , a condition that guarantees the L^pstability of the feedback system for any $p in [1,\\infty ]$ .

Keywords

Linear systems, time-invariant continuous-time; Stability; Algebra; Convolution; Delay; Feedback; Impulse testing; Laboratories; Laplace equations; Stability; System testing; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1972.1100180

Filename

1100180

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=810719