On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

TL;DR

This paper investigates the stability of linear control systems with sensor quantization using Krasovskii solutions, providing matrix inequality conditions and algorithms to ensure stability.

Contribution

It introduces new matrix inequality conditions for stability analysis of quantized systems using Krasovskii solutions and offers computational algorithms for practical implementation.

Findings

Conditions are always feasible if the quantization-free system is stable.

Proposed algorithms are computationally affordable.

Methodology is validated through three examples.

Abstract

Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.