On mean-square boundedness of stochastic linear systems with quantized observations

TL;DR

This paper introduces a method to design a finite-state quantizer and a bounded control policy for stochastic linear systems, ensuring the system's second moment remains bounded despite quantization.

Contribution

It presents a novel procedure for creating a state-quantizer with finitely many bins and a bounded policy to maintain mean-square boundedness in stochastic linear systems.

Findings

The proposed quantizer effectively manages quantized observations.

The bounded policy guarantees the second moment remains finite.

Applicable to marginally stable stochastic linear systems.

Abstract

We propose a procedure to design a state-quantizer with finitely many bins for a marginally stable stochastic linear system evolving in $\R^d$, and a bounded policy based on the resulting quantized state measurements to ensure bounded second moment in closed-loop.