Stability and <i>l</i><sub>∞</sub> Performance Analysis for Nabla Discrete Fractional Linear Positive System with Time-Varying Delays

Stability and <i>l</i><sub>∞</sub> Performance Analysis for Nabla Discrete Fractional Linear Positive System with Time-Varying Delays

In this paper, the stability and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mo>∞</mo></msub></semantics></math></inline-formula>-gain problem...

Full description

Saved in:

Bibliographic Details
Main Authors:	Cuihong Wang, Xueli Cui, Yanrong Cao, Yangquan Chen
Format:	Article
Language:	English
Published:	MDPI AG 2024-11-01
Series:	Fractal and Fractional
Subjects:	nabla discrete fractional system positive system time-varying delay stability <i>l</i>∞ performance
Online Access:	https://www.mdpi.com/2504-3110/8/11/660
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	In this paper, the stability and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mo>∞</mo></msub></semantics></math></inline-formula>-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the system’s positivity. Then, based on the system’s positivity property, an asymptotically stable condition is established. Furthermore, it is demonstrated that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mo>∞</mo></msub></semantics></math></inline-formula>-gain of such systems is determined by the system matrices and is independent of the magnitude of delays. Finally, numerical examples are provided to demonstrate the validity of the obtained results.
ISSN:	2504-3110