This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from un...This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.展开更多
It is proved that the set of all symmetric real matrices of order n with eigenvalues lying in the interval(α, β), denoted by Sn(α,β), is convex in Rn×n. With this result, some known results on positive(negati...It is proved that the set of all symmetric real matrices of order n with eigenvalues lying in the interval(α, β), denoted by Sn(α,β), is convex in Rn×n. With this result, some known results on positive(negative) definiteness, and Hurwitz(Shur) stability, as well as the aperiodic property of polytopes of symmetric matrices are generalized, and a series of insightful necessary and sufficient conditions for some general set of symmetric matrices contained in Sn(α,β) are presented,which are directly available for analysis of the positive(negative) definiteness, Hurwitz(Shur) stability and the aperiodic property of a wide class of sets of symmetric matrices.展开更多
This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the nex...This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R<sub>0</sub> α<sub>1</sub> and α<sub>2</sub>) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
The application of χ state are investigated in remote state preparation （RSP）. By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and ...The application of χ state are investigated in remote state preparation （RSP）. By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.展开更多
Suppression of noises is studied for the open-loop-closed-loop （OPCL） coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows...Suppression of noises is studied for the open-loop-closed-loop （OPCL） coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows bounds. The error signal can be decreased exponentially by enlarging the absolute value of the eigenvalues＇ real part of the Hurwitz matrix. A method is provided to reduce the error signal sufficiently and achieve complete synchronization （US） effectively for the OPCL coupling systems under noises. Based on this method, three numerical examples are reported in this paper,展开更多
Stability is a significant property for a robot hand grasp to perform complextasks similar to human hands. The common method to investigate the stability of roboticmulti-fingered grasp system is Lyapunov direct method...Stability is a significant property for a robot hand grasp to perform complextasks similar to human hands. The common method to investigate the stability of roboticmulti-fingered grasp system is Lyapunov direct method, but usually it is rather difficult toconstruct a proper Lyapunov function. Avoiding the hard work of constructing a Lyapunov function, wepropose the sufficient conditions for stability of the robotic grasp system.展开更多
基金supported by National Basic Research Program of China (973 Program) (No. 6138101004-3)Key Project of Innovation Knowledge of Chinese Academy of Sciences (No. YYYJ-0917)Innovation Knowledge of Chinese Academy of Sciences (No.O7A6210601)
文摘This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.
文摘It is proved that the set of all symmetric real matrices of order n with eigenvalues lying in the interval(α, β), denoted by Sn(α,β), is convex in Rn×n. With this result, some known results on positive(negative) definiteness, and Hurwitz(Shur) stability, as well as the aperiodic property of polytopes of symmetric matrices are generalized, and a series of insightful necessary and sufficient conditions for some general set of symmetric matrices contained in Sn(α,β) are presented,which are directly available for analysis of the positive(negative) definiteness, Hurwitz(Shur) stability and the aperiodic property of a wide class of sets of symmetric matrices.
文摘This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R<sub>0</sub> α<sub>1</sub> and α<sub>2</sub>) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
基金supported by the National Natural Science Foundation of China(Grant Nos.61201253 and 61303039)the Fundamental Research Funds for the Central Universities of China(Grant No.2682014CX095)
文摘The application of χ state are investigated in remote state preparation （RSP）. By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.
文摘Suppression of noises is studied for the open-loop-closed-loop （OPCL） coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows bounds. The error signal can be decreased exponentially by enlarging the absolute value of the eigenvalues＇ real part of the Hurwitz matrix. A method is provided to reduce the error signal sufficiently and achieve complete synchronization （US） effectively for the OPCL coupling systems under noises. Based on this method, three numerical examples are reported in this paper,
文摘Stability is a significant property for a robot hand grasp to perform complextasks similar to human hands. The common method to investigate the stability of roboticmulti-fingered grasp system is Lyapunov direct method, but usually it is rather difficult toconstruct a proper Lyapunov function. Avoiding the hard work of constructing a Lyapunov function, wepropose the sufficient conditions for stability of the robotic grasp system.
