Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive a...Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.展开更多
The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active be...The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equiv...This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.展开更多
Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning ...Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.展开更多
This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,s...This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.展开更多
This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fu...This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this cond...The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.展开更多
This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principl...This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principle. The result obtained generalizes those in known literatures.展开更多
In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov fu...In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov function is avoided.展开更多
In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stabi...In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stability is obtained. The method is illustrated with an example and it is compared with other methods proposed in the literature. The results have applications in the filter design.展开更多
According to a class of nonlinear SISO discrete systems, the fiizzy sliding mode control problem is considered. Based on Takagi-Sugeno fuzzy model method, a fuzzy model is designed to describe the local dynamic perfor...According to a class of nonlinear SISO discrete systems, the fiizzy sliding mode control problem is considered. Based on Takagi-Sugeno fuzzy model method, a fuzzy model is designed to describe the local dynamic performance of the given nonlinear systems. By using the sliding mode control approach, the global controller is constructed by integrating all the local state controllers and the global supervisory sliding mode controller. The tracking problem can be easily dealt with by taking advantage of the combined controller,and the robustness performance is improved finally. A simulation example is given to show the effectiveness and feasibility of the method proposed.展开更多
Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih'lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix ine...Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih'lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix inequality (LMI) approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify the validity of the proposed method.展开更多
In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.
This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncerta...This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H<sub><sub></sub></sub><sub>∞</sub> state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H<sub><sub><sub></sub></sub></sub><sub>∞</sub> noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.展开更多
The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
The restricted flows of a hierarchy of discrete integrable systems are presented. It is shownthat integrals of motion and Lax representation for restricted flows as well as a discrete zerocurvature representation for ...The restricted flows of a hierarchy of discrete integrable systems are presented. It is shownthat integrals of motion and Lax representation for restricted flows as well as a discrete zerocurvature representation for the hierarchy with sources can be deduced from the zero-curvaturerepresentation for the hierarchy. Also it is studied how the hierarchy is related to the AKNShierarchy in the continuous limit.展开更多
This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetit...This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.展开更多
We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discre...We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.10372054 and 70431002)
文摘Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.
文摘The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
文摘This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.
基金supported by the National Natural Science Foundation of China(U21A20166)in part by the Science and Technology Development Foundation of Jilin Province (20230508095RC)+1 种基金in part by the Development and Reform Commission Foundation of Jilin Province (2023C034-3)in part by the Exploration Foundation of State Key Laboratory of Automotive Simulation and Control。
文摘Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.
基金supported by National Natural Science Foundation of China (grant No.41874132)supported by National Natural Science Foundation of China (grant No.11201173)+3 种基金National Natural Science Foundation of China (grant No.11171132,grant No.11571065)Science and Technology Developing Plan of Jilin Province (grant No.20180101220JC)supported by National Basic Research Program of China (grant No.2013CB834100)Jilin DRC (grant No.2017C028-1)。
文摘This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.
基金This research was supported by the National Natural Science Foundation of China under Grant No.61903167.
文摘This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.
基金Supported by National Natural Science Foundation of China (50977008, 60904017, 60774048, 60728307), the Funds for Creative Research Groups of China (60521003), the Program for Cheung Kong Scholars and Innovative Research Team in University (IRT0421), and the 111 Project (B08015), National High Technology Research and Development Program of China (863 Program) (2006AA04Z183)
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
基金the Natural Science Foundation of China (60774011)the Natural ScienceFoundation of Zhejiang Province in China (Y105141)
文摘The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.
基金Supported by the Project-sponsored by SRF for ROCS, SEM of China(48371109) the Natural Science Foundation of Hebei Province (A2006000941).
文摘This paper concerns a class of impulsive discrete systems and offers sufficient conditions of boundedness in terms of two measures for such systems, by employing vector Lyapunov functions and a new comparison principle. The result obtained generalizes those in known literatures.
文摘In this paper, the stability of nonlinear time-delay discrete systems is investigated bymeans of the Gauss-Seidel iteration method. Some algebraic criteria of the stability are obtained. Theconstruction of Lyapunov function is avoided.
文摘In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stability is obtained. The method is illustrated with an example and it is compared with other methods proposed in the literature. The results have applications in the filter design.
基金This work was supported by the National Natural Science Foundation of China (No, 60274099)the Doctoral Dissertation Foundation of Northeastern University (No. 200308).
文摘According to a class of nonlinear SISO discrete systems, the fiizzy sliding mode control problem is considered. Based on Takagi-Sugeno fuzzy model method, a fuzzy model is designed to describe the local dynamic performance of the given nonlinear systems. By using the sliding mode control approach, the global controller is constructed by integrating all the local state controllers and the global supervisory sliding mode controller. The tracking problem can be easily dealt with by taking advantage of the combined controller,and the robustness performance is improved finally. A simulation example is given to show the effectiveness and feasibility of the method proposed.
文摘Based on Lyapunov stability theory, a less conservative sufficient condilions for the stabih'lies of uncertain discrete delayindependent and delay-dependent control systems are obtained by using the linear matrix inequality (LMI) approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify the validity of the proposed method.
基金Supported by the National Natural Science Foundation of China(Grant No.11601011)
文摘In this paper, we study two kinds of first-order singular discrete systems. By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.
文摘This paper investigates the problem of robust optimal H<sub>∞</sub> control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H<sub><sub></sub></sub><sub>∞</sub> state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H<sub><sub><sub></sub></sub></sub><sub>∞</sub> noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
文摘The restricted flows of a hierarchy of discrete integrable systems are presented. It is shownthat integrals of motion and Lax representation for restricted flows as well as a discrete zerocurvature representation for the hierarchy with sources can be deduced from the zero-curvaturerepresentation for the hierarchy. Also it is studied how the hierarchy is related to the AKNShierarchy in the continuous limit.
基金supported by National Natural Science Foundation of China(Nos.61273070 and 61203092)111 project(No.B12018)
文摘This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given.
基金supported by the Key Program of National Natural Science Foundation of China(Grant No.11232009)the National Natural Science Foundation ofChina(Grant Nos.11072218,11272287,and 11102060)+2 种基金the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)the Natural ScienceFoundation of Henan Province,China(Grant No.132300410051)the Educational Commission of Henan Province,China(Grant No.13A140224)
文摘We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.