In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the ...In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the disturbance attenuation problem is constructed for uncertain nonlinear cascaded systems with internal stability.展开更多
The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differenc...The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.展开更多
The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the shor...The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction o[ some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.展开更多
文摘In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the disturbance attenuation problem is constructed for uncertain nonlinear cascaded systems with internal stability.
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.
基金Supported by the National 973 Project 2012 CB927402the National Natural Science Foundation under Grant Nos.11074145 and 61275028
文摘The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction o[ some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.