Separation Principle for a Class of Nonlinear Feedback Systems Augmented with Observers

In English The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an input nonlinearity in the feedback path. Provided that the system using state feedback satisfies the circle criterion (i.e., when all states can be measured), we show that stability of the extended system with output feedback control from a (full state) Luenberger-type observer may be concluded using the circle criterion. As another result, we state a separation principle for a class of feedback systems with an input nonlinearity.When only local stability results can be stated, our method provides an estimate of the region of attraction.