Quasi-ISS reduced-order observers and quantized output feedback

We formulate and study the problem of designing nonlinear observers whose error dynamics are input-to-state stable (ISS) with respect to additive output disturbances as long as the plant´s input and state remain bounded. We present a reduced-order observer design which achieves this quasi-ISS property when there exists a suitable state-independent error Lyapunov function. We show that our construction applies to several classes of nonlinear systems previously studied in the observer design literature. As an application of this robust observer concept, we prove that quantized output feedback stabilization is achievable when the system possesses a quasi-ISS reduced-order observer and a state feedback law that yields ISS with respect to measurement errors. A worked example is included.