Feedback is a most important concept in control systems, its main purpose is to deal with internal and/or external uncertainties in dynamical systems, by using the on-line observed information. Thus, a fundamental problem in control theory is to understand the maximum capability and potential limits of the feedback mechanism. This paper gives a survey of some basic ideas and results developed recently in this direction, for several typical classes of uncertain dynamical systems including parametric and nonparametric nonlinear systems, sampled-data systems and time-varying stochastic systems.
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