Stability analysis of time–varying perturbed descriptor systems

Faten Ezzine; Mohamed Ali Hammami; Walid Hdidi

doi:10.3934/jcd.2024007

Article Contents

2024, Volume 11, Issue 2: 174-188. Doi: 10.3934/jcd.2024007

This issue Previous Article Towards optimal space-time discretization for reachable sets of nonlinear control systems Next Article Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime

Stability analysis of time–varying perturbed descriptor systems

1.
University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Tunisia
2.
Jouf University, College of Sciences and Arts of Tabrjal, Department of Mathematics, Saudi Arabia
3.
University of Kairouan, Higher Institute of Applied Mathematics and Computer Science of Kairouan, Tunisia

^*Corresponding author: Faten Ezzine
^*Corresponding author: Faten Ezzine

Received: January 2023

Revised: January 2024

Early access: February 2024

Published: April 2024

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Abstract

The manuscript deals with the analytical study of the "practical" stability of linear time dependent descriptor perturbed systems. The paper works out and proves the sufficient conditions (posed as LMIs) for practical stability of perturbed singular systems. The Gamidov's type integral inequality is used as a tool in the proof of the sufficient conditions of practical stability for perturbed singular systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

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Mathematics Subject Classification: Primary: 37B55; Secondary: 34D20.

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Figure 1. The initial response of the nominal descriptor system (4.2), with the initial condition $ x_0 = [1, 0]^T $

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Figure 2. The initial response of the perturbed singular system (4.1), with the initial condition $ x_0 = [1, 0]^T $

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Figure 3. The initial response of the nominal descriptor system (4.4), with the initial condition $ x_0 = [1, 0]^T $

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Figure 4. The initial response of the perturbed descriptor system (4.3), with the initial condition $ x_0 = [1, 0]^T $

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