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Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems

✍ Scribed by Daniel E. Frank; Samuel A. Musa

Publisher: Elsevier Science
Year: 1972
Tongue: English
Weight: 665 KB
Volume: 294
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(72)90011-7

No coin nor oath required. For personal study only.

✦ Synopsis

The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-var@ag gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k, + k,(t) + k,(t) g( .) where g(a) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-var&g gains are

Ll(O, 03) functctions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the ouptut of the system, is also employed to determine the settling time.

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