Exponential Stability of a Robot with Safety System

This paper presents the analysis of exponential stability of a system consisting of a robot and its associated safety mechanism. The system have various modes of failures and is repairable. The paper investigates the nonnegative stead-state solution of system,the existence of strictly dominant eigenvalue and restriction of essential spectrum growth bound of the system operator. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that the dynamic solution of the system is exponential stab＇flity and converges to the steady-state solution.     

Exponential Stability Analysis of a Markovian Deteriorating System

The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of the exponential stability of such a system requires the application of functional analysis and, particularly, the theory of linear operators in Banach space to demonstrate the existence of strictly dominant eigenvalue. Through analyzing the variation of the essential spectral radius of semigroups before and after perturbation, it is shown that the dynamic solution of the system converges to the steady-state solution of the system exponentially under certain condition.     

Exponential Stability of a Reparable System with Two Types of Repair Facilities

The exponential stability of a reparable system with two types of repair facilities is discussed in this paper. We present that the c0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.     

Exponential Stability of a Muti-state Device Redundant System with Common-cause Failures and One Standby Unit

In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.     

EXPONENTIAL STABILITY OF A REPARABLE MULTI-STATE DEVICE

The exponential stability of a multi-state device is discussed in this paper. We present that the Co-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue O.     

具分布延时细胞神经网络的指数周期与稳定性

研究了具分布延时细胞神经网络的全局指数周期性与指数稳定性。在没有假设激活函数是有界的、可微的、单调增的情况下,通过应用一些新的分析技巧与Halanay-type不等式方法,得到了确保延时细胞神经网络周期解存在唯一且全局指数周期与全局指数稳定的简单的、容易验证的、新的充分条件。并给出了算例及其仿真结果支持所得结论。     

时滞切换系统指数稳定性分析：Lyapunov-Krasovskii泛函方法

考虑由两个线性时滞子系统构成的切换系统,分析其在任意切换序列作用下保持指数稳定性的条件.分别利用二次型与逐段二次型的Lyapunov-Krasovskii泛函构造方式给出了以线性矩阵不等式所表述的稳定性判据;进而通过状态变量代换结合积分不等式技巧证明了指数衰减率对于所有切换序列一致成立,即其完全取决于系统的结构特征.最后给出了一个算例.     

一类延时细胞神经网络的指数周期性与稳定性

细胞神经网络动态行为的研究是细胞神经网络应用的理论基础。对一类具分布延时细胞神经网络,研究了其全局指数周期性与稳定性。在输出函数满足全局Lipschitz连续的条件下,通过构造合适的Lyapunov泛函,给出了延时细胞神经网络全局指数周期性与稳定性的容易验证的充分条件。给出了算例及其仿真结果来验证所得结论,并说明所得结论与文献[16]的结论是相互独立的。     

Exponential Stability of Interval Time-Varying Dynamical System with Multidelay

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Global Exponential Stability of Variable Delay and Time－varying Measure Differential Systems with Impulse Effect

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一类可修的人机系统解的渐近稳定性

研究了两相同部件温储备可修的人机系统,利用由该系统所决定的算子A+B生成的Banach空间中的正压缩C0半群,证明了此系统的非负稳定解恰是算子A+B的.本征值对应的本征向量,同时通过研究算子A+B的谱特征,得到了算子A+B的谱点均位于复平面的左半平面且在虚轴上除0点外无谱的结论,进而得到了该系统的渐近稳定性.     

时滞随机线性大系统的指数稳定性

针对一般随机线性时滞微分方程，给出了方程的平凡解的几乎必然指数稳定性的一个充分条件，由此利用时滞随机系统的比较原理建立一般时滞随机线性大系统的二阶矩指数稳定与几乎必然指数稳定新的代数判据．利用恰当的Lyapunov函数结合不等式技巧得到了这些条件．特别是用一个代数方程给出了依赖时滞的Lyapunov指数的估计．并用实例加以验证．     

STABILITY CRITERIA FOR A CLASS OF UNCERTAINSYSTEMS WITH TIME—DELAY

Some stability criteria are obtained for a class of uncertain systems with time-delay usingLyapunov functional and analytic techniques. It is easy to check the criteria by making use of theboundedness of the uncertainties.     

Reliability and Numerical Analysis of a Robot Safety System

This paper discusses a model for a repairable robot safety system composed of a safety component and two redundant robots according to a semi-group approach. The development of the model is divided into three phases:(Ⅰ) The use of pure analysis to prove the uniqueness of a classical solution to the model;(Ⅱ) The verification of this uniqueness by providing a non-negative solution to the model; and(Ⅲ) the formulation of reliability indices for the model, along with numerical examples to explain the results. The existence, uniqueness, and exponential stability of the solution of the repairable robot safety system is studied using Volterra-type integral-differential-equation theory, and the spectral distribution of the ACP operator is discussed. Moreover, the authors propose a method to investigate the steady-state indicator of the robot safety system with the safety component working, and with or without the component revolving, to make use of the correspondence of the eigenvector to the eigenvalue zero. The authors show that the robot's operation, with or without the safety component revolving and with fractional motion, is superior to that with the safety component working. The novelty of the approach lies in its examination of a unique solution to the system and its exponential stability based on C_0-semi-group theory, the co-final relative theory, and the functional analysis method.     

Availability Analysis of a Repairable Series-Parallel System with Redundant Dependency

This paper investigates the steady-state availability of a repairable series-parallel system with redundant dependency. The different types of components and repairmen are taken into account,the failure rate of the operating component varies as the number of other failed components and the repair rate of the failed component is constant in each parallel redundant subsystem. To quantify the redundant dependency, a modified failure dependence function is introduced to determine the failure rate of the components in each subsystem. Markov theory and matrix analysis method are used to get the steady-state probability vector of each subsystem and the steady-state availability of the entire system. A numerical example is presented to illustrate the obtained results and to analyze the effect of redundant dependency class on the system availability.     

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.     

The Stabilization of Discrete Time Singular VariableStructure System with Disturbance

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两部件并联维修系统解的渐近稳定性

研究了两部件并联维修系统,在系统非负解存在惟一的基础上,利用系统算子生成的Banach空间中的正压缩C0半群,证明了系统的非负稳定解恰是系统算子0本征值对应的非负本征向量.同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性.     

双稳系统数值仿真模型的稳定性分析

数值仿真方法是双稳系统输出特性研究中经常使用的方法。双稳系统离散模型的稳定性分析是对其进行数值仿真研究的基础．以前的研究未能给出模型的稳定性条件。通过理论推导，分析并得到了双稳系统数值仿真模型在不同参数取值下的稳定性条件．在此基础上进行了数值仿真试验，数值仿真结果与理论分析结果相一致，为双稳系统数值仿真研究时的参数选择提供了依据。     

带阻容负载的能量存储系统建模与稳定性分析

阻容负载提高了能量存储系统阶次,对稳定性不利。为分析其稳定性,建立了降压模式下带阻容性负载的状态空间平均模型、小信号与大信号等效电路模型;通过分析小信号模型进行了系统补偿,提高了稳定裕量;通过大信号模型验证了补偿系统在大扰动下的稳定性。针对Simulink中无理想交直流变压器模块,提出了一种理想交直流变压器模型构造方法,还提出了一种新颖的基于此构造方法的负载参数动态仿真模型,可解决Simulink中动态参数负载仿真困难问题。这里建立的阻容性负载模型精度可与宏模型基本一致,但仿真效率远高于宏模型。