Input-to-state stabilization with quantized output feedback

We study control systems where the output subspace is covered by a finite set ofquantization regions, and the only information available to a controller is which of thequantization regions currently contains the system's output. We assume the dimension of theoutput subspace is strictly less than the dimension of the state space. The number ofquantization regions can be as small as 3 per dimension of the output subspace. We show how todesign a controller that stabilizes such a system, and makes the system robust to an externalunknown disturbance in the sense that the closed-loop system has the Input-to-State Stabilityproperty. No information about the disturbance is required to design the controller. Achievingthe ISS property for continuous-time systems with quantized measurements requires a hybridapproach, and indeed our controller consists of a dynamic, discrete-time observer, acontinuous-time state-feedback stabilizer, and a switching logic that switches between severalmodes of operation. Except for some properties that the observer and the stabilizer must possess,our approach is general and not restricted to a specific observer or stabilizer. Examples ofspecific observers that possess these properties are included.