Wirtinger-based Exponential Stability for Time-Delay Systems

TL;DR

This paper introduces a Wirtinger-based inequality approach to achieve exponential stabilization of time-delay systems, providing new stability criteria, controller synthesis, and observer-based control methods with numerical validation.

Contribution

It presents a novel stability theorem using Wirtinger inequalities and extends it to controller and observer design for time-delay systems.

Findings

Theorem guarantees exponential decay-rate for time-delay systems.

Numerical comparisons show improved stabilization results.

Extension of existing stability criteria to control synthesis.

Abstract

This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided. Variations of this theorem for synthesis of a controller or for an observer-based control is derived. Some numerical comparisons are proposed with existing theorems of the literature and comparable results are obtained but with an extension to stabilization.