On the capability of feedback for unknown nonparametric systems with input delay

It is well-known that feedback is a central concept in control systems, and that to understand the capability of the feedback mechanism is a fundamental issue in control theory. In general, the feedback capability depends on the nature of uncertainty, the structure of nonlinearity, and the timely use of information. Although much effort has been made in understanding the maximum capability of feedback in recent years, the case where there is a pure time-delay in the feedback channel remains to be unexplored, which appears to be highly nontrivial. In this paper, we shall investigate the capability of feedback mechanism for a basic class of discrete-time uncertain nonparametric nonlinear dynamical systems with delayed feedback, and provide a sufficient condition for global feedback stabilization in terms of the Lipschitz constant for the uncertain class of Lipschitz functions, and reveal how the time-delay in the feedback channel influences the feedback capability.