ON THE GLOBAL ATTRACTIVITY FOR A NEUTRAL DIFFERENCE EQUATION WITH TWO DELAYS

ＯＮ　ＴＨＥ　ＧＬＯＢＡＬ　ＡＴＴＲＡＣＴＩＶＩＴＹ　ＦＯＲ　Ａ　ＮＥＵＴＲＡＬ　ＤＩＦＦＥＲＥＮＣＥ　ＥＱＵＡＴＩＯＮ　ＷＩＴＨ　ＴＷＯ　ＤＥＬＡＹＳＯＮＴＨＥＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＦＯＲＡＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴ...     

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

ＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＡＲＩＳＩＮＧＦＲＯＭＥＶＡＰＯＲＡＴＩＯＮＦＲＯＭＰＯＲＯＵＳＭＥＤＩＵＭＹＡＮＧＬＩＰＩＮＧ（杨力平）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅ...     

UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

ＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦ２－ＤＩＭＥＮＳＩＯＮＡＬＭＡＧＮＥＴＯＨＹＤＲＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＳＺＨＡＮＧＬＩＮＧＨＡＩＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

CONVERGENCE AND STABILITY OF SOLUTIONSOF CERTAIN INFINITE DELAY DIFFERENTIAL EQUATIONS

ＣＯＮＶＥＲＧＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＯＦＣＥＲＴＡＩＮＩＮＦＩＮＩＴＥＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＺｈｅｎｇＢｕｎａｎ＆ＣｈｅｎＷｕｈｕａ＆ＬｕｏＧｕｉｌｉｅ（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉ...     

CONVERGENCE AND STABILITY OF SOLUTIONS OF CERTAIN INFINITE DELAY DIFFERENTIAL EQUATIONS

ＣＯＮＶＥＲＧＥＮＣＥＡＮＤＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＯＦＣＥＲＴＡＩＮＩＮＦＩＮＩＴＥＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣｈｅｎＷｕｈｕａ（ＧｕａｎｇＸｉＮａｔｉｏｎａｌＩｎｓｔｉｔｕｔｅ，Ａｂｓｔｒａｃｔ：ＢｙＣｏ...     

UNIQUENESS AND ITERATIVE METHOD OF POSITIVE RADIALLY SYMMETRIC SOLUTIONS FOR SINGULAR ELLIPTIC EQUATIONS

ＵＮＩＱＵＥＮＥＳＳＡＮＤＩＴＥＲＡＴＩＶＥＭＥＴＨＯＤＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＬＹＳＹＭＭＥＴＲＩＣＳＯＬＵＴＩＯＮＳＦＯＲＳＩＮＧＵＬＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＺｈａｏＺｅｎｇｑｉｎ（赵增勤）（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅ...     

ON GLOBAL SOLUTION FOR A CLASS OF SYSTEMS OF MULTI－DIMENSIONAL GENERALIZED ZAKHAROV TYPE EQUATION

ＯＮＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＳＹＳＴＥＭＳＯＦＭＵＬＴＩ－ＤＩＭＥＮＳＩＯＮＡＬＧＥＮＥＲＡＬＩＺＥＤＺＡＫＨＡＲＯＶＴＹＰＥＥＱＵＡＴＩＯＮＧＵＯＢＯＬＩＮＧ（郭柏灵）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄａｎｄＣｏｍｐｕ...     

ASYMPTOTIC BEHAVIOR OF NONOSCILLATORY SOLUTIONS OF A SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＮＯＮＯＳＣＩＬＬＡＴＯＲＹＳＯＬＵＴＩＯＮＳＯＦＡＳＥＣＯＮＤＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（孟繁伟）曲阜师范大学，邮编：２７３１６５ＭｅｎｇＦａｎｗｅｉ（ＱｕｆｕＮ...     

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM(III)_(m=0)HAVING THREE ANTI-SADDLES(II)

ＬＩＭＩＴＣＹＣＬＥＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＣＵＲＶＥＳＦＯＲＴＨＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭ（ＩＩ）ｍ＝０ＨＡＶＩＮＧＴＨＲＥＥＡＮＴＩＳＡＤＤＬＥＳ（Ｉ）ＹＥＹＡＮＱＩＡＮＡｂｓｔｒａｃｔＡｓａｃｏｎｔｉ...     

UNIFORMLY VALID ASYMPTOTIC APPROXIMATIONS FOR NONLINEAR SINGULARLY－PERTURBED VECTOR BOUNDARY VALUE PROBLEMS

ＵＮＩＦＯＲＭＬＹＶＡＬＩＤＡＳＹＭＰＴＯＴＩＣＡＰＰＲＯＸＩＭＡＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＳＩＮＧＵＬＡＲＬＹ－ＰＥＲＴＵＲＢＥＤＶＥＣＴＯＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳ￥ＳｈｉＹｕｍｉｎｇ（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓ...     

REGULARIZATION OF SINGULAR SYSTEMS BY OUTPUTFEEDBACK

1.IntroductionInthispaper,weconsideralineartime--invariaflt'system{EI;," "(1)withthematricesE,AER",BER"m,CeRP",alldEissingular.Thebehaviorofasingularsystemdependscriticallyontheeigenstructureofthepencil(E,A).Tilepencil(E,A)andthecorrespondingsystem(1)aresaidtoberegularifdet(orE--dA)/0forsome(a,0)eCZ(2)andtheyaresaidtohaveindexatmostoneifthedimensionofthelargestnilpotelltblock(whichcorrespondstoaninfinitepole)intheKroneckercanonicalformofthepencil(E,A)islessthanorequalto..e[3'12]…     

State feedback and output feedback control of a class of nonlinear systems with delayed measurements

This paper is concerned with the problem of state feedback and output feedback control of a class of nonlinear systems with delayed measurements. This class of nonlinear systems is made up of continuous-time linear systems with nonlinear perturbations. The nonlinearity is assumed to satisfy a global Lipschitz condition and the time delay is assumed to be time-varying and have no restriction on its derivative. On the basis of the Lyapunov–Krasovskii approach, sufficient conditions for the existence of the state feedback controller and the output feedback controller are derived in terms of linear matrix inequalities. Methods of calculating the controller gain matrices are also presented. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Balancing singular discrete-time systems

In this work, we deal with normalizable-balanced singular systems, that is, singular systems where the obtained closed-loop system is balanced by an appropriate feedback. In the invariant case, we use a proportional and derivative feedback to obtain systems without infinite poles. In addition, the existence and construction of state-feedbacks to obtain normalizable-balanced N-periodic singular systems is analyzed.     

New Algorithm for Computing LQ Suboptimal Output Feedback Gains of Decentralized Control Systems

In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.     

On output feedback control of singularly perturbed systems

We treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback controller, we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter. This condition, which is less restrictive than those previously given in the literature, is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and/or sensors. Furthermore, we show explicitly that, in the linear time-invariant case, if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system.     

Regularization of differential-algebraic equations

Linear systems of ordinary differential equations with an identically singular or rectangular matrix multiplying the derivative of the unknown vector function are numerically solved by applying the least squares method and Tikhonov regularization. The deviation of the solution of the regularized problem from the solution set of the original problem is estimated depending on the regularization parameter.     

Robust finite-time H∞ control of singular stochastic systems via static output feedback

This paper addresses the problem of robust finite-time stabilization of singular stochastic systems via static output feedback. Firstly, sufficient conditions of singular stochastic finite-time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Then the results are extended to singular stochastic H_∞ finite-time boundedness for the class of singular stochastic systems. Designed algorithm for static output feedback controller is provided to guarantee that the underlying closed-loop singular stochastic system is singular stochastic H_∞ finite-time boundedness in terms of strict linear matrix equalities with a fixed parameter. Finally, an illustrative example is presented to show the validity of the developed methodology.     

Boundary-Value Problems for Second-Order Equations and for Systems of First-Order Equations

The oblique derivative problem for harmonic functions under violation of the Shapiro–Lopatinsky condition is considered as well as some multi-dimensional analogues of the Cauchy–Riemann system. These problems are reduced to nonelliptic pseudo-differential equations. A method generalizing the regularization of singular integral equations is also presented.     

广义控制系统的动态阶配置

本文考虑广义控制系统。通过使用输出导数反馈配置系统的动态阶。     

Regularized collocation method for Fredholm integral equations of the first kind

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness.