This paper is concerned with the global stabilization of state-dependent switching neural networks(SDSNNs)viadiscontinuous event-triggered control with network-induced communication delay.Aiming at decreasing triggeri...This paper is concerned with the global stabilization of state-dependent switching neural networks(SDSNNs)viadiscontinuous event-triggered control with network-induced communication delay.Aiming at decreasing triggering times,a discontinuous event-trigger scheme is utilized to determine whether the sampling information is required to be sent outor not.Meanwhile,under the effect of communication delay,the trigger condition and SDSNNs are transformed into twotractable models by designing a fictitious delay function.Then,using the Lyapunov–Krasovskii stability theory,someinequality estimation techniques,and extended reciprocally convex combination method,two sufficient criteria are established for ensuring the global stabilization of the resulting closed-loop SDSNNs,respectively.A unified framework isderived that has the ability to handle the simultaneous existence of the communication delay,the properties of discontinuousevent-trigger scheme,as well as feedback controller design.Additionally,the developed results demonstrate a quantitativerelationship among the event trigger parameter,communication delay,and triggering times.Finally,two numerical examples are presented to illustrate the usefulness of the developed stabilization scheme.展开更多
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From ...The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.展开更多
In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equi...In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.展开更多
The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and inputadditive uncertainties is studied in this paper. The relative models with saturation nonlinear...The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and inputadditive uncertainties is studied in this paper. The relative models with saturation nonlinearity are established based on ClohesseyWiltshire equation. Considering the advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing high gain scheduling technique, a new robust gain scheduling controller is proposed to solve the robust global stabilization problem. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved.Different from the controller design, simulations have been carried out directly on the nonlinear model of the spacecraft rendezvous operation instead of a linearized one. The effectiveness of the proposed approach is shown.展开更多
This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain...This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.展开更多
A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equi...A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r<sub>0</sub> is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r<sub>0</sub> is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.展开更多
This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz crit...This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .展开更多
This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delay...This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.展开更多
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent, Our stabilizer consists of a nested saturation function, which is a nonlinear combinati...We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent, Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above,展开更多
In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.展开更多
A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved b...A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of ...The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent lit...In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.展开更多
This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical ...This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.展开更多
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u...In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.展开更多
An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input ...An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium and the endemic equilibrium are obtained. In the existence of input of infectious individuals, the models have no disease-free equilibrium. For corresponding SIR model, the endemic equilibrium is globally asymptotically stable; for corresponding SIRS model, the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62003194,61973199,61573008,and 61973200).
文摘This paper is concerned with the global stabilization of state-dependent switching neural networks(SDSNNs)viadiscontinuous event-triggered control with network-induced communication delay.Aiming at decreasing triggering times,a discontinuous event-trigger scheme is utilized to determine whether the sampling information is required to be sent outor not.Meanwhile,under the effect of communication delay,the trigger condition and SDSNNs are transformed into twotractable models by designing a fictitious delay function.Then,using the Lyapunov–Krasovskii stability theory,someinequality estimation techniques,and extended reciprocally convex combination method,two sufficient criteria are established for ensuring the global stabilization of the resulting closed-loop SDSNNs,respectively.A unified framework isderived that has the ability to handle the simultaneous existence of the communication delay,the properties of discontinuousevent-trigger scheme,as well as feedback controller design.Additionally,the developed results demonstrate a quantitativerelationship among the event trigger parameter,communication delay,and triggering times.Finally,two numerical examples are presented to illustrate the usefulness of the developed stabilization scheme.
基金This project was supported by the National Natural Science Foundation of Fujian province (A0510025) .
文摘The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
文摘In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.
基金supported by the Innovative Team Program ofthe National Natural Science Foundation of China(No.61021002)National Basic Research Program of China(973 Program)(No.2012CB821205)
文摘The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and inputadditive uncertainties is studied in this paper. The relative models with saturation nonlinearity are established based on ClohesseyWiltshire equation. Considering the advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing high gain scheduling technique, a new robust gain scheduling controller is proposed to solve the robust global stabilization problem. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved.Different from the controller design, simulations have been carried out directly on the nonlinear model of the spacecraft rendezvous operation instead of a linearized one. The effectiveness of the proposed approach is shown.
基金the National Natural Science Foundation of China (Grant No.60674036)the Science and Technique Development Plan of Shandong Province (Grant No.2004GG4204014)+2 种基金the Program for New Century Excellent Talents in University of China (Grant No.NCET-07-0513)the Excellent Young and Middle-Aged Scientist Award Grant of Shandong Province of China (Grant No.2007BS01010)the Key Science and Technique Foundation of Ministry of Education (Grant No.108079)
文摘This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.
文摘A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r<sub>0</sub> is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r<sub>0</sub> is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.
文摘This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .
基金supported via funding from Prince Sattam bin Abdulaziz University Project Number(PSAU/2023/R/1444)The first author is partially supported by the University Research Fellowship(PU/AD-3/URF/21F37237/2021 dated 09.11.2021)of PeriyarUniversity,SalemThe second author is supported by the fund for improvement of Science and Technology Infrastructure(FIST)of DST(SR/FST/MSI-115/2016).
文摘This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.
文摘We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent, Our stabilizer consists of a nested saturation function, which is a nonlinear combination of saturation functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above,
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.
基金supported by the National Natural Science Foundation of China (60474015)Program for Changjiang Scholars and Innovative Research Team in University
文摘A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
文摘The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
基金supported by Scientific Research(c),No.24540219 of Japan Society for the Promotion of Sciencesupported by Grant-in-Aid for Research Activity Start-up,No.25887011 of Japan Society for the Promotion of Science
文摘In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.
基金supported by the National Natural Science Foundation of China(10971166,10901131)the National High Technology Research and Development Program of China(863 Program,2009AA01A135)the Natural Science Foundation of Xinjiang Province(2010211B04)
文摘This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.
文摘An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium and the endemic equilibrium are obtained. In the existence of input of infectious individuals, the models have no disease-free equilibrium. For corresponding SIR model, the endemic equilibrium is globally asymptotically stable; for corresponding SIRS model, the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.