A dynamical inequality for the output of uncertain nonlinear systems

An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties. Although some progresses have been achieved in this area, they are all focused on some special classes of linearly parameterized nonlinear uncertain systems. In this paper, we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters. This inequality will be established using a stochastic imbedding approach based on a Cramér-Rao inequality for dynamical systems, and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.