converse theorem for practical $h$-stability of time-varying nonlinear systems

Damak, H.; Hammami, M. A.; Kicha, A.

doi:10.53733/79

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Based on this, Pinto first introduced the concept of h-stability and obtained the stability result of weakly stable systems under certain perturbations [24]. The h-system, also known as h-stability, is a special type of differential equation system, which is mainly used to study the weak stability of the system [25][26][27][28]. h-stability takes into account the sensitivity of system response to time step length and space step length, and allows stability constraints to be relaxed.…”

Section: Introductionmentioning

confidence: 99%

A direct analysis method to global h-stability of positive Cohen-Grossberg neural networks with time-varying delays

Sun

2023

Preprint

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In this paper, global h-stability of nonlinear positive Cohen-Grossberg neural network (PCGNN) system with time-varying delays is studied by means of a direct analysis method. By selecting the appropriate h function and determining its differential expression, global h-stability is converted into two types of known stability, that is Lagrangian exponential stability and global exponential stability. For the sake of improving the accuracy of the stability results, we spare no effort to optimize the fitting effect of the system state trajectory by changing the differential expression of the h function. In addition, two examples are given to verify the feasibility and effectiveness of this method in PCGNN.

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Section: Introductionmentioning

confidence: 99%

A direct analysis method to global h-stability of positive Cohen-Grossberg neural networks with time-varying delays

Sun

2023

Preprint

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A direct analysis method to globalh‐stability of delayed time‐varying nonlinear positive systems

Cao

Zhang

2022

Intl J Robust & Nonlinear

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This paper focuses on the global h-stability of the nonlinear positive system with multiple time-varying delays. Through differentiated expressions of the function h, the global h-stability could be referred to as several known stabilities, including Lagrange stability, asymptotic stability, global exponential stability, global practical stability, and so forth. By proposing a direct analysis method that differs from the so-called Lyapunov-Krasovskii functional method, we presented a sufficient condition for the global h-stability of such system. The obtained stability condition appeared in the form of a number of simple inequalities, which could be easily handled by the toolbox YALMIP loaded in MATLAB. The applicability of our results have been illustrated by three numerical examples. K E Y W O R D Sa direct analysis method, global h-stability, multiple time-varying delays, nonlinear time-varying positive systems

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On Uniform h-stability of Non-autonomous Evolution Equations in Banach Spaces

Damak¹

2021

Bull. Malays. Math. Sci. Soc.

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converse theorem for practical $h$-stability of time-varying nonlinear systems

Cited by 4 publications

References 17 publications

A direct analysis method to global h-stability of positive Cohen-Grossberg neural networks with time-varying delays

A direct analysis method to global h-stability of positive Cohen-Grossberg neural networks with time-varying delays

A direct analysis method to globalh‐stability of delayed time‐varying nonlinear positive systems

On Uniform h-stability of Non-autonomous Evolution Equations in Banach Spaces

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