On persistently exciting observers and a non-linear separation principle: application to the stabilization of a generator

We provide a separation principle for a class of non-linear time-varying systems. The only assumption we make on the state feedback control law is that it does not vanish as the states grow unboundedly. For the observer, we propose a design method based on the assumption that the system is transformable into a form affine in the unmeasured variable and a property of persistency of excitation. This assumption covers but is not restricted to the common observability condition that the vector field multiplying the unmeasured variable is separated from zero for all state values. Our separation principle relies on stability results for cascades systems.