We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves r...We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.展开更多
This study deals with the irregular linear quadratic control problem governed by continuous time system with time delay.Linear quadratic(LQ)control for irregular Riccati equation with time delay remains challenging si...This study deals with the irregular linear quadratic control problem governed by continuous time system with time delay.Linear quadratic(LQ)control for irregular Riccati equation with time delay remains challenging since the controller could not be solved from the equilibrium condition directly.The merit of this paper is that based on a new approach of‘two-layer optimization’,the controller entries of irregular case with time delay are deduced from two equilibrium conditions in two different layers,which is fundamentally different from the classical regular LQ control.The authors prove that the irregular LQ with time delay is essentially different from the regular case.Specifically,the predictive controller bases on the feedback gain matrix and the state is given in the last part.The presented conclusions are completely new to our best knowledge.Examples is presented to show the effectiveness of the proposed approach.展开更多
Consider the transmission eigenvalue problem for the wave scattering by a dielectric inhomogeneous absorbing obstacle lying on a perfect conducting surface. After excluding the purely imaginary transmission eigenvalue...Consider the transmission eigenvalue problem for the wave scattering by a dielectric inhomogeneous absorbing obstacle lying on a perfect conducting surface. After excluding the purely imaginary transmission eigenvalues, we prove that the transmission eigenvalues exist and form a discrete set for inhomogeneous nonabsorbing media, by using analytic Fredholm theory. Moreover, we derive the Faber-Krahn type inequalities revealing the lower bounds on real transmission eigenvalues in terms of the media parameters. Then, for inhomogeneous media with small absorption, we prove that the transmission eigenvalues also exist and form a discrete set by using perturbation theory. Finally, for homogeneous media, we present possible components of the eigenvalue-free zone quantitatively, giving the geometric understanding on this problem.展开更多
基金supported by the Applied Mathematics Enhancement Program of Linyi University
文摘We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.
基金the Natural Science Foundation of Shandong Province under Grant Nos.ZR2018MF019 and ZR2019MF052the National Natural Science Foundation of China under Grant No.61873179。
文摘This study deals with the irregular linear quadratic control problem governed by continuous time system with time delay.Linear quadratic(LQ)control for irregular Riccati equation with time delay remains challenging since the controller could not be solved from the equilibrium condition directly.The merit of this paper is that based on a new approach of‘two-layer optimization’,the controller entries of irregular case with time delay are deduced from two equilibrium conditions in two different layers,which is fundamentally different from the classical regular LQ control.The authors prove that the irregular LQ with time delay is essentially different from the regular case.Specifically,the predictive controller bases on the feedback gain matrix and the state is given in the last part.The presented conclusions are completely new to our best knowledge.Examples is presented to show the effectiveness of the proposed approach.
基金supported by National Natural Science Foundation of China(Grant Nos.91330109,11421110002 and 11301075)the Fundamental Research Funds for the Central Universities(Grant No.KYLX-0082)
文摘Consider the transmission eigenvalue problem for the wave scattering by a dielectric inhomogeneous absorbing obstacle lying on a perfect conducting surface. After excluding the purely imaginary transmission eigenvalues, we prove that the transmission eigenvalues exist and form a discrete set for inhomogeneous nonabsorbing media, by using analytic Fredholm theory. Moreover, we derive the Faber-Krahn type inequalities revealing the lower bounds on real transmission eigenvalues in terms of the media parameters. Then, for inhomogeneous media with small absorption, we prove that the transmission eigenvalues also exist and form a discrete set by using perturbation theory. Finally, for homogeneous media, we present possible components of the eigenvalue-free zone quantitatively, giving the geometric understanding on this problem.
