Nonlinear Observers Robust to Measurement Disturbances in an ISS Sense

Hyungbo Shim, Daniel Liberzon

Research output: Contribution to journalArticlepeer-review


This paper formulates and studies the concept of quasi-Disturbance-to-Error Stability (qDES) which characterizes robustness of a nonlinear observer to an output measurement disturbance. 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. We use these conditions to show that several well-known observer designs yield qDES observers, while some others do not. Our results also enable the design of novel qDES observers, as we demonstrate with examples. 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.

Original languageEnglish (US)
Article number7088569
Pages (from-to)48-61
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 2016


  • Input-to-State Stability
  • Measurement Disturbance
  • Nonlinear Observer
  • Quantization
  • Robustness

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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