Nonlinear Observers Robust to Measurement Errors and Their Applications in Control and Synchronization

Abstract

In this talk we address the problem of designing nonlinear observers that possess robustness to output measurement errors. To this end, we introduce a novel concept of quasi-Disturbance-to-Error Stable (qDES) observer. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. This relates to a novel "asymptotic ratio" characterization of ISS which is of interest in its own right. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. Applications to synchronization of electric power generators and of chaotic systems in the presence of measurement errors will also be discussed.