Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

TL;DR

This paper develops a Lyapunov-Krasowskii functional approach to analyze the stability of nonlinear systems with quantized control and constant input delays, providing conditions for stability across various quantization densities.

Contribution

It introduces a novel stability analysis method for quantized nonlinear systems with delays, accommodating any quantization density and characterizing maximum delay tolerance.

Findings

Stability conditions valid for any quantization density.

Quantized feedback law designed with hysteresis to prevent chattering.

Maximum delay tolerance characterized as a function of quantization density.

Abstract

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.