Irregular Sampling, Active Observability, and Convergence Rates of State Observers for Systems with Binary-Valued Observations

This paper is concerned with state observer design of systems with binary-valued output measurements. First, observability of sampled systems is obtained under noise-free observations and arbitrary sampling times. It demonstrates that if the original system is observable, the sampled system is always observable whenever sampling density is larger than some critical frequency, independent of the actual time sequences. This result is then used to design switching time sequences and deduce active observability for systems with binary-valued output observations. Convergence of state estimates relies on some persistent excitation conditions that are usually required to hold. When observations become noise corrupted it is shown that by designing suitable switching time sequences certain convergence rates can always be obtained, which are explicitly derived.