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

Publisher Website
Google Scholar
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 p stability of the feedback system for any p \in [1,\infty] .

This publication has 8 references indexed in Scilit: