Explicit Form of Lyapunov Functions 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 the extended system with only output feedback control from a (full state) Luenberger-type observer also can apply to the Circle Criterion. As a consequence, 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.