In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique...This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.展开更多
This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model,which is the interconnection of a linear delayed dynamic syste...This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model,which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator,and covers several well-known neural networks,such as Hopfield neural networks,cellular neural networks(CNNs),bidirectional associative memory(BAM)networks,recurrent multilayer perceptrons(RMLPs).By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality(LMI)technique,some exponential synchronization criteria are derived.Using the drive-response concept,hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria.Finally,detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.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
The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluat...The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluation of error-correction capability and the synthesis procedures for continuous-time associative memory neural networks.展开更多
We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the...We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.展开更多
This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated proces...This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.展开更多
The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controller...The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.展开更多
Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomia...Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomial growth nonlinearity(?is arbitrary).展开更多
The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multipl...The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.展开更多
Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under satura...Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.展开更多
The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results ar...The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results are illustrated by wave and beam equations with simulation.展开更多
Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it ...Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.展开更多
This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.展开更多
This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an ...This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.展开更多
By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε...By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.展开更多
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep...In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.展开更多
This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter...This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.展开更多
In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof ar...In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .展开更多
In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,wh...In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,where the designed controller must guarantee the stability of the closed-loop system.The research approach undertaken in this paper assumes that the system state is known.We employ an integral-type feedback controller to achieve system stability,where the integral kernel function serves as a parameter.We attempt to select the corresponding exponentially stable system as the target system,and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system,thereby eliminating the adverse effects of time delays on the system.The crux lies in determining the equation that the kernel function must satisfy.Herein,we primarily present a methodology for selecting the parameter function within this transformation,to achieve an exponentially stable feedback controller.展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60774039,60974024,and 61074089CityU Research Enhancement Fund 9360127,CityU SRG 7002355
文摘This paper concerns with the master-slave exponential synchronization analysis for a class of general Lur'esystems with time delay.Different from the previous methods based on the differential inequality technique, a newapproach is proposed to derive some new exponential synchronization criteria.The restriction that the control widthhas to be larger than the time delay is removed.This leads to a larger application scope for our method.Moreover, notranscendental equation is involved in the obtained result, which reduces the computational burden.Two examples aregiven to validate the theoretical results.
基金Project supported in part by the National Natural Science Foundationof China (No. 60504024)the Specialized Research Fund for theDoctoral Program of Higher Education,China (No. 20060335022)+1 种基金theNatural Science Foundation of Zhejiang Province (No. Y106010),China the "151 Talent Project" of Zhejiang Province (Nos.05-3-1013 and 06-2-034),China
文摘This paper investigates the exponential synchronization problem of some chaotic delayed neural networks based on the proposed general neural network model,which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator,and covers several well-known neural networks,such as Hopfield neural networks,cellular neural networks(CNNs),bidirectional associative memory(BAM)networks,recurrent multilayer perceptrons(RMLPs).By virtue of Lyapunov-Krasovskii stability theory and linear matrix inequality(LMI)technique,some exponential synchronization criteria are derived.Using the drive-response concept,hybrid feedback controllers are designed to synchronize two identical chaotic neural networks based on those synchronization criteria.Finally,detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.
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Supported by the National Natural Science Foundation of Chinathe Climb Project of China
文摘The attraction domains of memory patterns and exponential convergence rate of the network trajectories to memory patterns for continuous feedback associative memory are estimated. These results can be used for evaluation of error-correction capability and the synthesis procedures for continuous-time associative memory neural networks.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.2013R1A1A2A10005201)the UAE University(Grant No.NRF Project UAEU-NRF-7-20886)
文摘We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.
基金partially supported by the Natural Science Foundation of China(11671134)
文摘This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.
基金This project was supported by the National Natural Science Foundation of China (No. 69674109).
文摘The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.
文摘Under the assumption that ?g(t) is translation bounded in , and using the method developed in [3], we prove the existence of pullback exponential attractors in ?for nonlinear reaction diffusion equation with polynomial growth nonlinearity(?is arbitrary).
基金Supported partially by the NSFC and the Science Foundation of China State Education Commission.
文摘The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered.It is proved that the system is exponentially stabilizable.The frequency domain method and the multiplier technique are applied.
基金supported by the National Natural Science Foundation of China(62173215)the Major Basic Research Program of the Natural Science Foundation of Shandong Province in China(ZR2021ZD04,ZR2020ZD24)
文摘Dear Editor,This letter presents a class of saturated sliding mode control (SMC)strategy for linear systems subject to impulsive disturbance and input saturation. To ensure the feasibility of proposed SMC under saturation, a relationship is established among attraction domain, saturation structure and control gain.
文摘The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results are illustrated by wave and beam equations with simulation.
文摘Parametric survival models are essential for analyzing time-to-event data in fields such as engineering and biomedicine.While the log-logistic distribution is popular for its simplicity and closed-form expressions,it often lacks the flexibility needed to capture complex hazard patterns.In this article,we propose a novel extension of the classical log-logistic distribution,termed the new exponential log-logistic(NExLL)distribution,designed to provide enhanced flexibility in modeling time-to-event data with complex failure behaviors.The NExLL model incorporates a new exponential generator to expand the shape adaptability of the baseline log-logistic distribution,allowing it to capture a wide range of hazard rate shapes,including increasing,decreasing,J-shaped,reversed J-shaped,modified bathtub,and unimodal forms.A key feature of the NExLL distribution is its formulation as a mixture of log-logistic densities,offering both symmetric and asymmetric patterns suitable for diverse real-world reliability scenarios.We establish several theoretical properties of the model,including closed-form expressions for its probability density function,cumulative distribution function,moments,hazard rate function,and quantiles.Parameter estimation is performed using seven classical estimation techniques,with extensive Monte Carlo simulations used to evaluate and compare their performance under various conditions.The practical utility and flexibility of the proposed model are illustrated using two real-world datasets from reliability and engineering applications,where the NExLL model demonstrates superior fit and predictive performance compared to existing log-logistic-basedmodels.This contribution advances the toolbox of parametric survivalmodels,offering a robust alternative formodeling complex aging and failure patterns in reliability,engineering,and other applied domains.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
文摘This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.
基金supported by National Natural Science Foundation of China(No.12171152)。
文摘By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。
文摘In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy.
基金supported by the Na⁃tional Key R&D Program of China(No.2022YFC2204800)the Graduate Student Independent Exploration and Innovation Program of Central South University(No.2024ZZTS 0767).
文摘This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.
基金supported by the NSFC(12271141)supported by the Fundamental Research Funds for the Central Universities(B240205026)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX24_0821).
文摘In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined onR^(N) . The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on R^(N) .
基金supported by the National Natural Science Foundation of China(No.12301579)the Fundamental Research Funds for the Central Universities of Civil Aviation University of China(No.3122019140).
文摘In this paper,we delve into the problem of exponential stability for a coupled system of a one-dimensional(1-D)N-root wave network with boundary delays.Our aim is to establish a universal controller design strategy,where the designed controller must guarantee the stability of the closed-loop system.The research approach undertaken in this paper assumes that the system state is known.We employ an integral-type feedback controller to achieve system stability,where the integral kernel function serves as a parameter.We attempt to select the corresponding exponentially stable system as the target system,and then construct a bounded linear transformation to demonstrate the equivalence between the target system and the original system,thereby eliminating the adverse effects of time delays on the system.The crux lies in determining the equation that the kernel function must satisfy.Herein,we primarily present a methodology for selecting the parameter function within this transformation,to achieve an exponentially stable feedback controller.
