# Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for $\sigma Ramarajan, S and Thathachar, M AL (1973) Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for$\sigma. In: SIAM Journal on Control and Optimization, 11 (1). pp. 94-99.

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## Abstract

For a feedback system consisting of a transfer function $G(s)$ in the forward path and a time-varying gain $n(t)(0 \leqq n(t) \leqq k)$ in the feedback loop, a stability multiplier $Z(s)$ has been constructed (and used to prove stability) by Freedman [2] such that $Z(s)(G(s) + {1 / K})$ and $Z(s - \sigma )(0 < \sigma < \sigma _ * )$ are strictly positive real, where $\sigma _ *$ can be computed from a knowledge of the phase-angle characteristic of $G(i\omega ) + {1 / k}$ and the time-varying gain $n(t)$ is restricted by $\sigma _ *$ by means of an integral inequality. In this note it is shown that an improved value for $\sigma _ *$ is possible by making some modifications in his derivation. ©1973 Society for Industrial and Applied Mathematics.

Item Type: Journal Article Copy right of this article belongs to Society for Industrial and Applied Mathematics. Division of Electrical Sciences > Electrical Engineering 06 Jan 2010 05:44 19 Sep 2010 05:46 http://eprints.iisc.ernet.in/id/eprint/23552