In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitio...In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.展开更多
This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii(L-K) functional is introduce...This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii(L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities(LMIs),which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.展开更多
The emergence of various new services has posed a huge challenge to the existing network architecture.To improve the network delay and backhaul pressure,caching popular contents at the edge of network has been conside...The emergence of various new services has posed a huge challenge to the existing network architecture.To improve the network delay and backhaul pressure,caching popular contents at the edge of network has been considered as a feasible scheme.However,how to efficiently utilize the limited caching resources to cache diverse contents has been confirmed as a tough problem in the past decade.In this paper,considering the time-varying user requests and the heterogeneous content sizes,a user preference aware hierarchical cooperative caching strategy in edge-user caching architecture is proposed.We divide the caching strategy into three phases,that is,the content placement,the content delivery and the content update.In the content placement phase,a cooperative content placement algorithm for local content popularity is designed to cache contents proactively.In the content delivery phase,a cooperative delivery algorithm is proposed to deliver the cached contents.In the content update phase,a content update algorithm is proposed according to the popularity of the contents.Finally,the proposed caching strategy is validated using the MovieLens dataset,and the results reveal that the proposed strategy improves the delay performance by at least 35.3%compared with the other three benchmark strategies.展开更多
This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is de...In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.展开更多
Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the s...Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the system. Firstly, the Takagi-Sugeno(T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system,and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities(LMIs). The effectiveness of the method is verified by simulation results.展开更多
This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forw...This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.展开更多
The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the s...The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer(LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output(BIBO) stability of the closedloop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.展开更多
This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and unive...This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and universal,a novel nonlinear predictive control method is proposed.The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays.At the same time,the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived.Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.展开更多
Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix...Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.展开更多
The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the...The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H∞ filter is derived in two methods： One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H∞ filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H∞ filtering problem in terms of the solutions of Riccati and matrix differential equations.展开更多
Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic m...Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.展开更多
The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evol...The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert space.Some sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential equations.The uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.展开更多
文摘In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii （LK） functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality （LMI） framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.
基金supported by National Natural Science Foundation of China(No.61074072)
文摘This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii(L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities(LMIs),which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.
基金supported by Natural Science Foundation of China(Grant 61901070,61801065,62271096,61871062,U20A20157 and 62061007)in part by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant KJQN202000603 and KJQN201900611)+3 种基金in part by the Natural Science Foundation of Chongqing(Grant CSTB2022NSCQMSX0468,cstc2020jcyjzdxmX0024 and cstc2021jcyjmsxmX0892)in part by University Innovation Research Group of Chongqing(Grant CxQT20017)in part by Youth Innovation Group Support Program of ICE Discipline of CQUPT(SCIE-QN-2022-04)in part by the Chongqing Graduate Student Scientific Research Innovation Project(CYB22246)。
文摘The emergence of various new services has posed a huge challenge to the existing network architecture.To improve the network delay and backhaul pressure,caching popular contents at the edge of network has been considered as a feasible scheme.However,how to efficiently utilize the limited caching resources to cache diverse contents has been confirmed as a tough problem in the past decade.In this paper,considering the time-varying user requests and the heterogeneous content sizes,a user preference aware hierarchical cooperative caching strategy in edge-user caching architecture is proposed.We divide the caching strategy into three phases,that is,the content placement,the content delivery and the content update.In the content placement phase,a cooperative content placement algorithm for local content popularity is designed to cache contents proactively.In the content delivery phase,a cooperative delivery algorithm is proposed to deliver the cached contents.In the content update phase,a content update algorithm is proposed according to the popularity of the contents.Finally,the proposed caching strategy is validated using the MovieLens dataset,and the results reveal that the proposed strategy improves the delay performance by at least 35.3%compared with the other three benchmark strategies.
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
文摘In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.
基金supported by the National Natural Science Foundation of China (61471323)。
文摘Considering packet losses, time-varying delay, and parameter uncertainty in the switched fuzzy system, this paper designs a robust fault detection filter at any switching rate and analyzes the H∞ performance of the system. Firstly, the Takagi-Sugeno(T-S) fuzzy model is used to establish a global fuzzy model for the uncertain nonlinear time-delay switched system,and the packet loss process is modeled as a mathematical model satisfying Bernoulli distribution. Secondly, through the average dwell time method and multiple Lyapunov functions, the exponentially stable condition of the nonlinear network switched system is given. Finally, specific parameters of the robust fault detection filter can be obtained by solving linear matrix inequalities(LMIs). The effectiveness of the method is verified by simulation results.
基金supported in part by the Natural Science Foundation of Heilongjiang Province (No.YQ2021F014)the Fundamental Research Funds for the provincial universities of Heilongjiang Province (No.2020-KYYWF-1040)。
文摘This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.
基金supported by the National Natural Science Foundation of China(NSFC)(61822311)the NSFC-Zhejiang Joint Fund for the Intergration of Industrialization and Informatization(U1709213)。
文摘The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer(LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output(BIBO) stability of the closedloop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.
基金This research was supported in part by the National Natural Science Foundation of China under Grant Nos.62173255 and 62188101.
文摘This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and universal,a novel nonlinear predictive control method is proposed.The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays.At the same time,the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived.Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.
基金Supported by the National Natural Science Foundation of China (6067402760875039)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education (20050446001)Scientific Research Foundation of Qufu Normal University
文摘Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.
基金supported by the National Natural Science Foundation for Distinguished Young Scholars of China under Grant No.60825304the National Basic Research Development Program of China under Grant No.973 Program,No.2009cb320600the National Natural Science Foundation of China under Grant No. 61104050
文摘The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H∞ filter is derived in two methods： One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H∞ filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H∞ filtering problem in terms of the solutions of Riccati and matrix differential equations.
基金supported by the National Natural Science Foundation of China(No. 51975274)National Key Laboratory of Science and Technology on Helicopter Transmission(Nanjing University of Aeronautics and Astronautics)(No. HTL-A-19K03)
文摘Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point.The parameters of the planetary gear system were optimized,and a two-dimensional nonlinear dynamic model was established using the lumped-mass method.Time-varying meshing stiffness was calculated by the energy method.The model consumes the backlash,bearing clearance,time-varying meshing stiffness,time-varying bearing stiffness,and time-varying friction coefficient.The time-varying bearing stiffness was calculated according to the Hertz contact theory.The load distribution among the gears was computed,and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication(EHL)theory.The dynamical equations were solved via numerical integration.The global bifurcation characteristics caused by the input speed,backlash,bearing clearance,and damping were analyzed.The system was in a chaotic state at natural frequencies or frequency multiplication.The system transitioned from a single-period state to a chaotic state with the increase of the backlash.The bearing clearance of the sun gear had little influence on the bifurcation characteristics.The amplitude was restrained in the chaotic state as the damping ratio increased.
基金supported by the National Natural Science Foundation of China under Grant No.61174081.
文摘The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert space.Some sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential equations.The uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.
