In this paper, we consider the problem of locally stabilizing non-linear systems by output feedback control. To be precise, the separation principle for non-linear Systems are studied, which allows the design of the control law and the observer to be carried out independently. While the previous results assumed' the existence of Lyapunov function for the observation error, we assume the existence of a state observer which asymptotically estimates the true state. As a matter of fact, it turns out that the latter condition is necessary for the former condition, but the converse is not true. The separation principle with the reduced order observer is also presented. Under the assumption that a non-linear system has asymptotically stable zero dynamics and is locally detectable, it is shown that the asymptotic output tracking by output feedback control can be achieved.
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