Stabilities and Settling Times of Nonlinear and Time-varying Feedback Systems |
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| Authors: | Daniel E Frank |
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| Institution: | Frankford Arsenal Philadelphia, Pennsylvania USA; Institute for Defense Analyses Arlington, Virginia USA |
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| Abstract: | The bounded-input bounded-output stability, finite time stability and settling time of a single-loop feedback system consisting of a nonlinear time-varying gain followed by a linear time-invariant system are investigated via a nonlinear integral inequality. The gain has the form k0+k1(t)+k2(t)g(bd) where g(bd) is a monotonic increasing function. The system is bounded-input bounded-output stable provided the time-varying gains are L1(0, t8) functions and is finite time stable for bounded gains. The nonlinear integral inequality, which is used to obtain explicit and useful bounds on the output of the system, is also employed to determine the settling time. |
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