1.

Absolute Stability of Lurie type Control System with Functional Equations





阮炯《数学年刊B辑(英文版)》,1983年第1期


In this paper,We give some sufficient conditions for absolute stability of the following controlsystems:We modify and generalize Theorems 2 and 4 in the paper[1]of A.Somolinos.

2.

NASCS FOR THE ABSOLUTE STABILITY OF LURE DIRECT CONTROL SYSTEMS





廖晓昕《数学物理学报(B辑英文版)》,1989年第1期


In this paper, we transform nth order Lure direct control systems into nonlinear systems with separating variables, and induce a concept for absolute stability of part arguments. The necessary and sufficient conditions (NASC) for the absolute stability of Lure direct control systems are given and some sufficient conditions are obtained

3.

Adaptive control of bifurcation and chaos in a timedelayed system





李宁 袁惠群 孙海义 张庆灵《中国物理 B》,2013年第22卷第3期


In this paper,the stabilization of a continuous timedelayed system is considered.To control the bifurcation and chaos in a timedelayed system,a parameter perturbation control and a hybrid control are proposed.Then,to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes,the adaptive control idea is introduced,i.e.,the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws,respectively.The adaptation algorithms are constructed based on the LyapunovKrasovskii stability theorem.The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods.They have the advantages of increased stability,adaptability to the changes of the system parameters,control cost saving,and simplicity.Numerical simulations for a wellknown chaotic timedelayed system are performed to demonstrate the feasibility and superiority of the proposed control methods.A comparison of the two adaptive control methods is also made in an experimental study.

4.

On the Simultaneous Approximation in Lpnorm





周颂平《数学研究与评论》,1984年第4期


Let C_[1,1]~(N) be the class of Nth continuously differentiable functions on [1,1], denote by L_(p[1,1]) the class of L_pintegrable functions on [1,1], E_n(f)_p is thebest approximation of f∈L_(p[1,1]) by nth algebraic polynomials, and C(·) is a positive constant only depending upon the quantities in the brackets. In Theorem 1, the condition that f(x)∈C_([1,1])~((N1)), f~((N1))(x) is absolutely continuous, and f~((N))(x)∈L_(p[1,1]) for N=O equals that f(x)∈L_(p[1,1]).

5.

EXISTENCE OF PERIODIC SOLUTIONS FOR A DISCRETETIME MODEL OF TWOCELL CNNS





Xiong Peiying Li Xuemei 《Annals of Differential Equations》,2006年第3期


We investigate a class of discretetime model of twocell cellular neural networks with symmetric template. By using the Lyapunov direct method, LaSalle's invariance principle, we discuss the existence and the stability of periodic solutions. The model considered has attractive 2periodic and unstable 2periodic solutions.

6.

ON THE UNCONDITIONAL ROBUST STABILITY FOR THE MULTIDELAYS INTERVAL COEFFICIENT CONTROL SYSTEM





黎野平 张少华 孟培源《Annals of Differential Equations》,2001年第2期


1 IntroductionIn [4] 5 Liu Yongqing discussed the equivalence problem about the closedloopcontrol system with delaysand the nodelay control systemin the stability theory, and obtained some sufficient criterion, where Al(i =1, 2), B, C are constants or timevarying matrices, h = hij 2 0(z, j = 1, 2,' 9 n).Recently, the stability and the unconditional stability about the controlsystem with delays and the delay neutral type control system, has been payingattention by many authors, and got m…

7.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF LIAPUNOV FUNCTION OF LUR'E FORM WITH■≤0





仵永先 赵素霞《应用数学学报(英文版)》,1990年第3期


This paper is concerned with the problem of absolute stability for a control system with severalexecutive elements. Necessary and sufficient conditions are obtained for the existence of Liapunovfunction of Lur'e form with negative semidefinite derivative (i.e. V≤0).

8.

ABSOLUTE STABILITY OF GENERAL LURIE TYPE INDIRECT CONTROL SYSTEMS 被引次数：3





甘作新 葛渭高 赵素霞 仵永先《应用数学学报(英文版)》,2001年第17卷第1期


1. IntroductionThe absolute stability problem is one of the central topics of the stability theory for itstheoretical and engineering importance. UP to date, this problem has been studied by manyauthors [19], and many sufficient conditions and some necessary and sufficiellt conditions inspecial cases for absolute stability are obtained. In papers [7,8], Liao gave a necessary andsufficient condition for absolute stability for partial arguments. In this paperg by using anew concept of absolut…

9.

具有常主曲率对称函数的超曲面





吴报强 宋鸿藻《数学季刊》,1994年第9卷第4期


Let M be a compact hypersurface is an(n 1)dimensional complete constant curvature space N(c),If Ricci curvature of Mis not less than max {0,(n1)c} and there is a constant main curvature function in M,then M can be classified completly,This is the Liebmann theorem in the widest sense so far.The methods used in this paper can be used to generalize a class of theorems with nonnegative (of positive)sectional curvature conditions.

10.

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS





陈继涛 吴启迪《应用数学和力学(英文版)》,2004年第25卷第3期


An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.

11.

Pinning control of complex Lur'e networks





张庆振 李忠奎《中国物理 B》,2009年第18卷第6期


This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur’e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur’e systems whose dimensions are the same as that of a single node. A circletype criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua’s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

12.

An Extension of the Turan Inequality in L_pspace for 0





周颂平《数学研究与评论》,1986年第2期


1. Introduction Denote by H_n. the set of nth algebraic polynomials all whose roots lie inside [1,1],R_n is the class of algebraic polynomials of degree n which have only real roots, and R_n~* is the class of trigonometric polynomials of degree n having only real zeros. Let C be a positive absolute constant, which may be different in different places.

13.

STABILITY ANALYSIS OF LARGESCALE SYSTEMS WITH MULTIPLE DELAYS





张钟俊 钱振英《数学物理学报(B辑英文版)》,1985年第3期


This paper is concerned with the stability analysis of a class of linear timeinvariant largescale systems with multiple delays. By using the properties of matrices, a sufficient condition of absolute stability is first derived for low order systems, described by differentialdifference equations. Then a comparison theorem is presented for differentialdifference inequalities. Finally, a sufficient condition of absolute stability for largescale systems with multiple delays is established by using the aggregation technique based on vector Lyapunov functions. A numerical example is also given to illustrate the applicability of the stability criterion obtained in this paper.

14.

A Supplement to the BaumKatzSpitzer Complete Convergence Theorem 被引次数：1





De Li LI Fu Xing ZHANG Andrew ROSALSKY《数学学报(英文版)》,2007年第23卷第3期


Let {X, Xn; n≥ 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n ≥ 1} be a sequence of positive constants such thatan↑∞ and 1〈 lim inf n→∞ a2n/an≤lim sup n→∞ a2n/an〈∞Set Sn=∑i=1^n Xi,n≥1.In this paper we prove that∑n≥1 1/n P（｜｜Sn｜｜≥εan）〈∞ for all ε〉0if and only if lim n→∞ Sn/an=0 a.s. This result generalizes the BaumKatzSpitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut.

15.

ABSOLUTE STABILITY OF GENERAL LURIE CONTROL SYSTEMS 被引次数：1





廖晓昕《数学物理学报(B辑英文版)》,1991年第1期


In this paper, we investigate the absolute stability of the general Lurie control systems. The necessary and sufficient conditions for absolute stability are obtained. These conditions can be readily checked and are convenient in application.

16.

On a New Class of SelfReferencing, 1/τ Atomic Clocks





王力军《中国物理快报》,2014年第8期


The merit of a modern atomic clock is measured by its phase stability. A clock＇s absolute timekeeping uncertainty typically worsens over its operating time τ as Δτα√τ, with an Allan deviation of sy σy（τ）=Δτ/τατ^1/2. Here we analyze a new class of selfreferencing clocks, whose phase is locked to itself after a certain time delay. We show that the Allan deviation of such clocks decreases as 1/τ over a long and controllable operating time. This class of clocks can maintain synchronization over a prolonged period with only a fixed, almost nonincreasing, absolute uncertainty, forming an ideal timepiece.

17.

Distortion Theorem for Bloch Mappings on the Unit Ball B^n





Jian Fei Wang and Tai Shun Liu《数学学报(英文版)》,2009年第25卷第10期


In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1  ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.

18.

Jackson’s theorem in Q_p spaces





CHEN YingWei & REN GuangBin 《中国科学 数学(英文版)》,2010年第2期


A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p < ∞, a > 1, and k1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute constant depending only on the parameter a.

19.

A Marcinkiewicz criterion for L~pmultipliers related to Schrdinger operators with constant magnetic fields





DENG Liu Rui MA Bo Lin LIU Shao Yue《中国科学 数学(英文版)》,2015年第2期


In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absolutely continuous on(0,∞)and ‖m‖∞+sup j∈Z2j 2i+1 rm′′(r)dr<∞,then the multiplier defined by m(t)is bounded on Lpfor 2n/(n+3)

20.

SEVERAL CRITERIONS OF ABSOLUTE STABILITY FOR THE SECOND CANONICAL FORM OF CONTROL SYSTEM





裘晓钢 舒仲周《应用数学和力学(英文版)》,1986年第9期


In this paper,several explicit criterions of absolute stability for the real secondcanonical form of control systemare given,which generalize and include the known result in ref.[2].By applying thesecriterions to the well known equations of the longitudinal motion of aircraft,a result thatgeneralizes and includes the known results in refs.[3,4,2]is obtained.
