Global Stability Analysis Non-Linear Systems

A special issue of J (ISSN 2571-8800). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 4881

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Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland
Interests: MATLAB simulation; modeling simulation; control theory; numerical modeling; system modeling; engineering mathematics; mathematical analysis; mathematical modelling; nonlinear analysis; advanced theory
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Special Issue Information

Dear Colleagues,

A dynamical system is called globally (absolutely) stable if it is asymptotically stable for all of the initial conditions. In this Special Issue, the global stability of nonlinear feedback standard and fractional order systems will be investigated. In general cases, the feedback systems consist of linear dynamical parts and static nonlinear elements with given nonlinear characteristics. Feedbacks can also be located in dynamical systems. The linear part can be any dynamical time-invariant or time varying system, standard or positive (state variables inputs and outputs are nonnegative), described by standard linear operators or by fractional order operators. Special attention will be devoted to fractional different orders of standard and positive descriptor linear systems as described by Caputo, Rieman–Liouville, or Grunwald–Letnikov type operators. The analyzed systems can be any of nature: mechanical, electrical, pneumatic, biological, economical, etc. Experimental and mathematical modelling results and verification of models are also welcome for this Special Issue.

Prof. Dr. Tadeusz Kaczorek
Guest Editor

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Keywords

  • Analysis
  • Global stability
  • Feedback system
  • Non-linear system
  • Positive system

Published Papers (2 papers)

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13 pages, 520 KiB  
Article
Global Stability and Exponential Decay of Processes in Nonlinear Feedback Systems with Different Fractional Orders
by Tadeusz Kaczorek and Łukasz Sajewski
J 2021, 4(3), 328-340; https://0-doi-org.brum.beds.ac.uk/10.3390/j4030025 - 12 Jul 2021
Viewed by 1401
Abstract
The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Sufficient conditions for the [...] Read more.
The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Sufficient conditions for the exponential decay of processes in fractional nonlinear systems are given. Procedures for computation of a gain matrix characterizing the class of nonlinear elements are proposed and illustrated by examples. Full article
(This article belongs to the Special Issue Global Stability Analysis Non-Linear Systems)
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15 pages, 3256 KiB  
Article
Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India
by Nita H. Shah, Ankush H. Suthar, Ekta N. Jayswal and Ankit Sikarwar
J 2021, 4(2), 86-100; https://0-doi-org.brum.beds.ac.uk/10.3390/j4020008 - 30 Apr 2021
Cited by 4 | Viewed by 2616
Abstract
In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact [...] Read more.
In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model’s transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown. Full article
(This article belongs to the Special Issue Global Stability Analysis Non-Linear Systems)
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