An impossibility theorem on sampled-data feedback of uncertain nonlinear systems

In this paper, we investigate a basic class of first order sampled-data feedback control systems with unknown nonlinear structure and with sampling rate not necessary fast enough, aiming at understanding the capability and limitations of the sampled-data feedback. We show that if the sampling rate is larger than the inverse of the "slope" of the uncertain nonlinear function multiplied by a constant (approx 4.757), then there exists no sampled-data control which can globally stabilize the prescribed class of uncertain nonlinear systems. This "impossibility theorem" improves on a recent result established by Xue and Guo (2002).