Local Halanay's inequality with application to feedback stabilization

Michael Malisoff; Frederic Mazenc

doi:10.3934/mcrf.2024026

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2025, Volume 15, Issue 2: 570-589. Doi: 10.3934/mcrf.2024026

This issue Previous Article Source identification problems for a class of subdiffusion equations with weak nonlinearities Next Article A unified approach for realization of discrete-time fractional-order proportional derivative controller for two classes of plant models

Local Halanay's inequality with application to feedback stabilization

Michael Malisoff^1, , and
Frederic Mazenc^2,

1.
Louisiana State University, USA
2.
INRIA EPI DISCO, L2S-CNRS-CentraleSupélec, France

^*Corresponding author: Frederic Mazenc
^*Corresponding author: Frederic Mazenc

Received: January 2024

Revised: June 2024

Early access: June 2024

Published: June 2025

The first author is supported by US National Science Foundation Grants 2009659 and 2308282.

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Abstract

We provide a local version of an approach to proving asymptotic stability that is based on Halanay's inequality. Our results are applicable to a family of nonlinear systems that contain state and input delays. We determine input-to-state stability inequalities when the systems contain additive uncertainty. We combine the results with an observer and a Gramian approach, to solve an output feedback stabilization problem. Our numerical examples illustrate how our theorems lead to new basin of attraction estimates.

Keywords:

Mathematics Subject Classification: Primary: 93C23, 93D05, 93D20, 93D25; Secondary: 39B72, 34D23, 34D05, 26A46, 26A48.

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