State Observers and Stabilization of Systems with Binary-Valued Observations

This paper introduces an observer for linear time invariant systems in continuous time whose outputs are measured only by binary-valued sensors. The traditional observers will fail in general, even if the system has a full-rank observability matrix. It is shown that by controlling the sensor threshold, it is always possible to cause the output to cross the sensor threshold within a designated time interval. Information on the time instants of threshold crossing is then used to develop state estimates. Convergence properties of the state observer are established. It is shown that by generating appropriate switching time sequences, state observers are convergent in the mean squares sense, with probability one, and exponentially. Combined with a state feedback using the state estimates, this state estimator leads to a stabilizing output feedback.