Abstract
We shall in this contribution study a class of first-order sampled-data control systems with unknown nonlinear structure and with sampling rate not necessary fast enough, aiming at understanding how stabilizability depends quantitatively upon the choice of the sampling rate and the size of the uncertainty. We shall show that if the unknown nonlinear function has a linear growth rate with its slope (denoted by L) being a measure of the size of uncertainty, then the sampling rate should not exceed 1/L multiplied by a constant (/spl ap/7.53) for the system to be globally stabilizable. If, however, the unknown nonlinear function has a growth rate faster than linear, and if the system is disturbed by noises modeled as the standard Brownian motion, then an example is given, showing that the corresponding sampled-data system is not stabilizable in general, no matter how fast the sampling rate is.
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