Finite/fixed-time Stabilization of Linear Systems with States Quantization

TL;DR

This paper introduces a homogeneity-based method for finite and fixed-time stabilization of linear systems with quantized states, ensuring stability under dense quantization through a logarithmic quantizer.

Contribution

It presents a new homogeneity-based approach and a sufficient condition for finite/fixed-time stabilization of LTI systems with quantized measurements.

Findings

Homogeneity-based stabilization guarantees finite/fixed-time stability.

Logarithmic quantizer with dense quantization achieves stability.

Numerical simulations validate theoretical results.

Abstract

This paper develops a homogeneity-based approach to finite/fixed-time stabilization of linear time-invariant (LTI) system with quantized measurements. A sufficient condition for finite/fixed-time stabilization of multi-input LTI system under states quantization is derived. It is shown that a homogeneous quantized state feedback with logarithmic quantizer can guarantee finite/fixed-time stability of the closed-loop system provided that the quantization is sufficiently dense. Theoretical results are supported with numerical simulations.