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Showing papers by "James Taylor published in 1970"


Journal ArticleDOI
TL;DR: In this article, the point-by-point stability criterion was replaced by an integral criterion based on the integral relation, which is a special case of the stability criterion of Popov's stability criterion.
Abstract: Previous extensions of the stability criterion of Popov [1] for systems with a stable linear time-invariant plant $G(s)$ followed by a nonlinear time-varying gain $k(t)f( \cdot )$ entailed the definition of nonlinearity classes $[ f( \cdot ) \in N]$ and corresponding frequency domain multipliers $Z_N (s)$ Then, defining a measure of nonlinearity \[ F_{\min } \equiv \mathop {\min }\limits_x \{ \frac{{xf( x)}}{{\int_0^x {f( z )dz} }} \} \] stability is ensured if $Z(s) \in Z_N (s)$ exists, such that (i) $G(s)Z(s)$ is strictly positive real, (ii) $Z(s - \Lambda ) \in Z_N (s)$ and (iii)\[\frac{1}{k}\frac{{dk}}{{dt}}\leqq \Lambda F_{\min } \quad ( {\text{see [ 5 ]}})\]In this paper, the point by point requirement of (iii) is replaced by an integral criterion In many cases the constraints on $k(t)$ predicated by the integral inequality are substantially less strict than those of (iii) above As (iii) is a special case of the integral relation, the results are never more strictThe development here will be li

5 citations