具有边界控制的线性Timoshenko型系统的指数稳定性

研究多孔弹性材料在实际应用中的稳定性问题.多孔物体的动力学行为由线性Timoshenko型方程描述,这样的系统一般只是渐近稳定但不指数稳定,假定系统在一端简单支撑,另一端自由,在自由端对系统施加边界反馈控制,讨论闭环系统的适定性和指数稳定性.首先,证明了由闭环系统决定的算子A是预解紧的耗散算子、生成C0压缩半群,从而得到了系统的适定性.进一步通过对系统算子A的本征值的渐近值估计,得到算子谱分布在一个带域,相互分离的,模充分大的本征值都是A的简单本征值.通过引入一个辅助算子A0,利用算子A0的谱性质以及算子A与A0之间的关系,得到了A的广义本征向量的完整性以及Riesz基性质.最后利用Riesz基性质和谱分布得到闭环系统的指数稳定性.     

泛函微分方程的弱指数渐近稳定性

本文提出一种新的稳定性概念,即弱指数渐近稳定,并给出两个关于弱指数渐近稳定的判别定理和一个较广泛的指数渐近稳定判别结果.从而使得许多具有一致渐近稳定性的解的趋零速度,得到了一种估计.文中还深入地揭露了一致渐近稳定性和弱指数渐近稳定性之间的内在联系以及弱指数渐近稳定性和指数渐近稳定性的关系.     

变时滞的退化中立型微分系统的稳定性

研究了具有变时滞的退化中立型微分系统的稳定性．利用退化时滞微分系统的变易公式和Gronwall-Bellman积分不等式给出了该系统的指数估计以及稳定和指数渐近稳定的充分条件．     

广义系统渐近稳定性的一种新的Lyapunov判别方法

本文中，对广义系统构造了一种新的Lyapunov函数，并给出相应的渐近稳定性的Laypunov判别方法。另外，我们证明了当广义系数为R－能稳时，必存在一反馈控制使得闭环系统为渐近稳定性的。     

具有动态边界的非均匀Euler-Bernoulli梁的边界反馈镇定

本讨论一端带有重物的Euler-Bernoulli梁的边界反馈镇定问题。在生物的质量忽略不计而只考虑重物的转动惯量的情况下，证明了同时在梁的自由端施加力和力矩反馈，闭环系统的能量可被指数镇定。进而对于系统只有力反馈或只有力矩反馈的情况，得到了闭环系统（指数）稳定的充分必要条件。     

具有扭转耦合效应的复合薄壁梁黎斯基的性质和指数稳定性(英文)

研究了具有扭转耦合效应的复合薄壁梁黎斯基的性质以及指数稳定性.首先证明该系统决定算子的预解式是紧的,且可生成群.其次,通过对该系统算子谱的渐近分析,证明了除至多有限个本征值外,其算子的谱是单重可分离的.特殊地,我们获得了自由系统的频率渐近表达式,因而利用克尔德什定理,证明了在希尔伯特状态空间中算子广义本征函数列的完备性.最后,结合黎斯基的性质及算子谱的分布证明了该系统的指数稳定性.     

参数变化下的广义指数二分性

本文对时间平移参数系统和时间尺度参数系统给出了广义指数二分性的判据，并且讨论了相应系统的极限方程的广义指数二分性．本文还通过分析广义指数二分性来探讨缓交系数系统和高频振荡系统的渐近稳定性与不稳定性．     

k/N:G冗余表决系统的渐近稳定性

分析了带有修理设备和多重致命及非致命操作故障的k／N(G)冗余表决系统的渐近稳定性．用该系统算子生成的正定C-半群证明了系统非负时间依赖解的存在唯一性．同时通过对系统算子谱点分布的分析，证明了本征值0对应的本征向量恰好是系统的静态解，并且，0是虚轴上系统算子唯一的谱点，从而证明了系统的渐近稳定性．     

脉冲时滞微分系统的弱指数渐近稳定性

研究了脉冲时滞微分系统的弱指数渐近稳定性.利用Razumikhin-Lyapunov函数方法得到系统弱指数渐近稳定的充分判据.提出"可脉冲弱指数镇定"及"脉冲控制模式"的概念.对一类较一般的n阶非线性脉冲时滞系统的脉冲镇定问题作了深入探讨.     

Timoshenko梁点反馈的稳定性

研究T im oshenko梁点反馈的稳定性.用线性算子半群方法证明了闭环系统的适定性,并应用算子谱特征得到了闭环系统的强渐近稳定性的充分必要条件.同时,给出了保守系统的几个能观性不等式.     

Stabilization of string system with linear boundary feedback

In this paper we consider the uniform stabilization of a vibrating string with Neumann-type boundary conditions. Herein we do not consider a controller stabilizing the system, but emphasize the simplicity and effectiveness of the controller. We adopt the linear feedback control law, which comprises both boundary velocity and position, and prove that the closed loop system is dissipative and asymptotically stable. By asymptotic analysis of frequency of the closed loop system, we give asymptotic expression of the frequencies and the Riesz basis property of eigenvectors and generalized eigenvectors of the system operator under some conditions, and hence obtain the exponential stability of the closed loop system. We show that, for a particular case, the system may be super-stable in subspace of a codimensional one. From the above result, we conclude that one can design a much simpler linear controller by choice of parameters such that the closed loop system is of Riesz basic properties and exponentially stable.     

两端固定n根系列连接的Timoshenko梁在连接点加控制的镇定问题

文章研究两端固定n根系列连接的Timoshen]K0梁系统的镇定问题,假设该系统在连接点处剪切力和弯曲力矩是连续的,而横向位移和旋转角度是不连续的.在连接点处设置控制器,观测节点处的力,通过补偿器补偿后反馈回系统,构成闭环系统.通过对系统的矩阵化处理,对算子谱采用渐近分析的技巧,证明得到该闭环系统是渐近稳定的.并利用算子谱的分布等性质,在一定条件下得到了闭环系统的Riesz基性质,从而系统满足谱确定增长条件.     

Stabilization of a one‐dimensional wave equation with variable coefficient under non‐collocated control and delayed observation

In this paper, we consider stabilization of a 1‐dimensional wave equation with variable coefficient where non‐collocated boundary observation suffers from an arbitrary time delay. Since input and output are non‐collocated with each other, it is more complex to design the observer system. After showing well‐posedness of the open‐loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed‐loop system is stable exponentially. Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non‐collocated control.     

BOUNDARY FEEDBACK STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH A TIPLOAD

g1. IntroductionThe purpose of this paPer is to study the stabilization problem of TimoshenkO beamattached with a load of mass M at one end and forced by linear boundary feedback conirols.The system to be investigated in this paper is described as follows (see [1] for example):lthe::1::1'{;::f'5'>', (11)Here u1(t) and u2(t) are the boundary feedback coatrols of force and momellt respectivelythe meanings of all the other variables, functions and coefficients aJre the same as thosedescribed in…     

Asymptotic behavior of Timoshenko beam with dissipative boundary feedback

This paper is concerned with the stabilization problem of Timoshenko beam in the presence of linear dissipative boundary feedback controls. Using C₀-semigroups theory we establish the existence and the uniqueness of solution of the proposed closed loop system. In order to consider the asymptotic behavior of the closed loop system, we first discuss the existence of nonzero solution of a closely related boundary value problem. Then we derive various necessary and sufficient conditions for the system to be asymptotically stable. Finally, we prove the equivalence between the exponential stability and the asymptotic stability for the closed loop system.     

Timoshenko梁的边界反馈一致镇定

该文研究在Timoshenko梁两端施加边界反馈控制的镇定问题.在某些线性边界反馈作用下,通过分析闭环系统算子的谱,并利用频域方法证明了相应的闭环系统的一致稳定性.     

Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls

In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.     

Non‐linear Control of a Hydraulic Piston Actuator without Velocity Information

The mathematical models of hydraulic actuators are known to be non‐linear. Therefore, in order to increase the dynamic performance of the closed‐loop system, we have to take into account the significant non‐linearities of the hydraulic plant in the controller design. In this contribution, we deal with so‐called valve‐controlled translational piston actuators. In general, they have the pleasing property to be exact input‐to‐state linearizable in the sense of the differential geometric control synthesis approach. However, in practical applications it often turns out that those controllers, which have to rely on the knowledge of the piston velocity, have problems in the case of noisy measurements. This is why, we propose an approach where the non‐linear controller is designed in such a way that the control law is independent of the piston velocity. It can be even proven that the closed‐loop system is globally asymptotically stable.     

Synthesis of linear systems with desired equivalent form

A method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed loop system matrix is proposed. The method is based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form. A stable computational algorithm for finding the serial canonical form using orthogonal similarity transformations is described. The algorithm for synthesis involves a simple recurrent procedure and gives the possibility to achieve any attainable equivalent form of the closed loop system. The results obtained are extended to the synthesis of reduced order state observers.