Stability Analysis of Positive Systems With Bounded Time-Varying Delays

Liu, Xingwen; Yu, Wensheng; Wang, Long

doi:10.1109/tcsii.2009.2023305

Cited by 157 publications

(3 citation statements)

References 19 publications

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“…Linear systems have been studied extensively and have yielded rich results from early on. The class of positive linear systems has also been actively researched in recent years by mathematicians [4] [5] [6] [7]. Various stability criteria for this class of systems have been pro-posed, including necessary and sufficient conditions for positive linear systems without delays and with constant delays.…”

Section: Introductionmentioning

confidence: 99%

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

Tuan

2024

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Section: Introductionmentioning

confidence: 99%

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

Tuan

2024

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“…Fractional calculus is recognized as a compelling framework by researchers, offering the potential to yield more precise outcomes in the realms of science and technology. [21][22][23][24] To clarify, its heightened flexibility in comparison to classical calculus can be attributed to its hereditary attributes and utilization of memory-based representations. Riemann and Liouville introduced the fundamental concept of fractional order (FO) differentiation in reference 25.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

Jan,

Boulaaras,

Alnegga

et al. 2023

Int J Numerical Modelling

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Typhoid fever poses a severe hazard to public health and affects at least 27 million people annually around the globe. It is significant to conceptualize the key factors of the transmission phenomena of this bacterial infection. We formulate a novel epidemic model for typhoid fever with vaccination and carriers via Caputo‐Fabrizio operator. The fundamental results of the model are inspected analytically and the basic reproduction value are then assessed. The Jacobian matrix approach has been used to demonstrate the local stability of the infection‐free steady‐state for . We interrogated the uniqueness and existence of the solution of the recommended fractional dynamics of typhoid fever. We illustrated the solution pathways of the recommended system of typhoid fever numerically and demonstrated the dynamics of the infection with variation of different parameters. Our results demonstrated how the dynamical behavior of the typhoid fever infection is influenced by input parameters. The findings highlight the significance and persuasive behavior of fractional order and show that the model's fractional memory effects appear to be a good fit for these kinds of findings. We have shown the most attractive factors of the system for the control and prevention through our study.

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“…For example, non-negative and compartmental models, which consist of homogeneous interconnected compartments that exchange non-negative quantities of materials, are typical positive systems and play a key role during many processes in biology and medical science. The feature that the state variables of positive systems are limited to a cone, not the entire space makes the study of positive systems interesting and challenging (Hu et al, 2017(Hu et al, , 2019Liu et al, 2009;Qi and Gao, 2016).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and L1-gain characterization of positive sampled-data systems

Hu,

Shi,

Sun

2023

Transactions of the Institute of Measurement and Control

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In this study, the positive stability and [Formula: see text]-gain characterization problem are investigated for positive sampled-data systems. By constructing a new sampling-period-dependent copositive Lyapunov functional, and introducing the free weight matrix method to remove the single integral term, sufficient conditions for the asynchronous stability of the positive sampled-data system are established. Furthermore, system disturbances that occur frequently in engineering are taken into account. Conditions for robust stability of positive sampled-data systems that satisfy [Formula: see text]-gain performance are developed in the form of the linear programming technology. A numerical example and a practical simulation based on a communication network model are provided to illustrate the rationality and application of the theoretical results.

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Stability Analysis of Positive Systems With Bounded Time-Varying Delays

Cited by 157 publications

References 19 publications

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

Stability analysis and L1-gain characterization of positive sampled-data systems

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