ON FUZZY STABILITY OF L-FUZZY SYSTEMS

The concepts of λ-stability, λ-fuzzy stability, λ-uniform stability, and λ-fuzzy uniform stability of L-fuzzy systems are introduced. Several equivalent conditions are given. The relation between the concepts and that of continuity of mappings from a topological space into a topological space is studied. A few open questions are posed.     

THE CATEGORY THEORY OF TIME SYSTEMS

In this paper we show a categorical treatment of general time systems using the categorization method presented in our previous paper. Various concepts about general time systems are categorized in the unified framework. Some category theoretical tools for the investigation of such time systems are presented. Using those tools some basic properties of time systems are explored in our framework. In particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms. These results show that our method can be a universal tool for a categorization and a categorical treatment of mathematically defined general systems.     

广义不确定系统稳定鲁棒控制

利用李雅普诺夫稳定理论和矩阵范数性质研究了广义不确定系统的稳定鲁棒控 制问题.在不同情况下,分别给出了保证闭环不确定系统渐进稳定的两类稳定鲁棒控制:状态 反馈、正常动态补偿器的设计方法,得到了鲁棒稳定控制的不确定量的范数界,而且提出了在 多个稳定鲁棒控制器中寻找具有最大的不确定量范数界的控制器的方案.     

结构不确定性系统的敏感性分析

讨论了控制对象和控制器同时存在稳定反馈结构不确定性的鲁棒稳定性和性能敏 感性问题,给出了摄动系统鲁棒稳定的充分条件,得到了敏感函数矩阵和闭环传递函数矩阵 H∞的摄动上界.这里控制器并不要求是真稳定的,因此得到的结果较有一般性.     

单饱和输入下二阶控制系统零解全局渐近稳定的充分条件

分析了单饱和输入下控制系统的相空间分布规律并给出了具体的饱和输入下非线性 控制系统的空间结构.通过给出的空间结构与饱和输入下非线性控制系统的关系定义了不同于 一般意义下的非线性系统的平衡点,并且对新平衡点进行了分类.在此基础上,给出了二阶单饱 和输入下控制系统零解全局渐近稳定的充分条件,同时也给出了二阶单饱和输入下控制系统闭 合轨迹存在与否的判别条件.     

On Gnutella topology dynamics by studying leaf and ultra connection jointly in phase space

In this paper, the topology dynamics of Gnutella are studied in phase space. The dynamic progress of peer degree is studied as a time series in two dimensional phase space, which is consisted of numbers of connected leaves and ultras. The reported degrees concentrate on three special software related regions which we name as ultra stable region, leaf stable region and transition belt. A method is proposed on how to classify degree traces in phase space into different categories. Then the connection churn and the degree churn are studied. It shows that the topological structure of Gnutella is more stable in its connection degree than in the topology itself. The connection drop rate is estimated and the lifetime of connections is deduced afterwards. M/M/m/m loss queue system is introduced to model the degree keeping process in Gnutella. This model reveals that the degree stability is ensured by mass new connection efforts. In other words, the stability in topological structure of Gnutella is the results of many essential unstable factors in its topology. We think it raises a challenge to the basic design philosophy for such networks.     

一种评定步行机稳定性的新方法及其应用

本文提出了用稳定角和稳定行程作为步行机稳定性的评价指标，讨论了稳定角，稳定行程与稳定裕量、能量稳定裕量之间的关系，分析了步行机在坡道上沿任意方向行走的稳定性及其越坡能力，提出了描述步行机稳定状况的稳定区域图。     

无穷维时滞系统的变结构控制

本文在Banach空间研究了无穷维时滞系统的变结构控制问题,给出了滑动模态的稳定性条件,滑动模态的到达条件和变结构控制的一般形式,最后用分布参数系统变结构控制的例子说明了方法的有效性。     

Hybrid approach for the design of robust control systems

This paper addresses the problem of robust controller design for stable finite dimensional linear time-invariant systems (stable FDLTIS) within the framework of model reference schemes. The proposed methodology applies to both continuous and discrete-time systems and employs two distinct design stages: (1) design of the feedforward controller and (2) design of the feedback filter. Algebraic and topological concepts are utilized to tackle several important design issues including stability, performance and robustness. Finally, two examples are given to demonstrate the power of the design method.     

TOWARDS A GLOBAL ANALYSIS OF SYSTEMS

In this paper a topological approach to the analysis or properties or systems is outlined and accounted for, which is called a Global Analysis of Systems (GAS). Let a topological space t of system; and a property P of systems from Σ be given. Define Σ _p = {σ∈Σ; σ has the properly P}. Then the main question of the Global Analysis of Systems is: how can Σ _p , be characterized in topological terms? We claim that three types of properties are worthy of being distinguished from this topological point of view. They are called structural, generic and residual properties, if I, appears to be an open, open and dense, and residual subset of I respectively. A motivation for the Global Analysis of Systems flowing from differential geometry, theory of dynamical systems, catastrophe theory and the theory of control systems is presented. In conclusion a significance of the Global Analysis of Systems, both far systems theory and for a better understanding of the fundamental relation Model—Reality, is discussed.     

Razumikhin stability theorems for a general class of stochastic impulsive switched time‐delay systems

This paper studies stability of a general class of impulsive switched systems under time delays and random disturbances using multiple Lyapunov functions and fixed dwell‐time. In the studied system model, the impulses and switches are allowed to occur asynchronously. As a result, the switching may occur in the impulsive intervals and the impulses can occur in the switching intervals, which have great effects on system stability. Since the switches do not bring about the change of the system state, we study two cases in terms of the impulses, ie, the stable continuous dynamics case and the stable impulsive dynamics case. According to multiple Lyapunov‐Razumikhin functions and the fixed dwell‐time, Razumikhin‐type stability conditions are established. Finally, the obtained results are illustrated via a numerical example from the synchronization problem of chaotic systems.     

两足步行机器人动态步行姿态稳定性及姿态控制

本文提出了一种新型两足步行机器人动态步行实时控制方法，引入了姿态稳定性和步态稳定性的概念，把两足动态步行控制分为姿态稳定性控制和步态稳定性控制两个相互联系的子系统，并从姿态稳定性分析出发，重点研究了各关节轨迹跟踪控制和系统整体动态平衡等问题，提出了姿态控制器的结构及设计方法．     

STRONG STABILIZATION OF MIMO SYSTEMS: A PROJECTION APPROACH

In this paper, the strong stabilization problem of multivariable linear time‐invariant systems is considered. The approach is based on state‐space stable projection. The formulation is reduced to find a full rank constant output feedback. The computations involved are simpler than other methods.     

线性时变系统有限时间稳定性分析

针对一般非线性时变系统的有限时间稳定性分析问题,考虑到系统初始时刻在有限时间区间内的变化,本文分别提出了一般非线性时变系统的一致有限时间稳定性,一致收缩稳定性和固定调节时间一致收缩稳定性定义.针对一类线性时变系统,基于计算系统的所有轨线的包线的思想,本文分别给出了判定该类系统的收缩稳定性、固定调节时间收缩稳定性、一致有限时间稳定性、一致收缩稳定性、固定调节时间一致收缩稳定性的充分必要条件,同时给出了判定该类系统一致收缩稳定性及固定调节时间一致收缩稳定性的3个充分条件.进一步,本文将所得定理结果推广到了周期线性时变系统,所得结论为判定周期线性时变系统关于任意初始时刻的一致有限时间稳定性,一致收缩稳定性及固定调节时间一致收缩稳定性提供了理论依据.最后,以4个数值算例和两航天器相对运动过程为例验证了本文结果的正确性.     

Linear Generalized Synchronization of Spatial Chaotic Systems

This paper is devoted to study the generalized synchronization of spatial chaotic systems by applying linear coupling. Based on the stability of the fixed point of a plane system, we obtain the stable domain of the space plane. According to the stable domain of the space plane, the stable domain of the coupling strength for the linear generalized synchronization of the spatial chaotic systems is determined. Moreover, the relationship between the stable fixed plane and the synchronization of the spatial chaos system is also analyzed. Finally, an example is presented to validate the scheme and the analysis.     

Semi‐global finite‐time observers for multi‐output nonlinear systems

Finite‐time stability is investigated for nonlinear systems, which satisfy uniqueness of solution. First, a new sufficient condition for local finite‐time stability is presented. Next, by using the high‐gain observers and carefully selecting the homogeneity powers and weights, the problem of semi‐global and finite‐time stable observers is studied for multi‐output nonlinear systems with uniform observability and a triangular structure. Then, a design procedure is worked out for such observers. Finally, two numerical examples further verify the validity of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite Time Stability Analysis of Switched Systems with Stable and Unstable Subsystems

In this paper, we study the finite time stability of nonlinear switched systems consisting of both stable and unstable subsystems. First, the finite time stability of systems is studied using the activation time of the subsystems. We show that if the total activation time of unstable subsystems is relatively small compared with that of finite time stable subsystems, then finite time stability of switched systems is guaranteed. Second, the finite time stability of systems is studied based on the comparison principle. We show that if the comparison system is finite time stable, then the finite time stability of switched systems is guaranteed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed methods.     

REMARKS ON THE CONCEPT OF DYNAMICAL SYSTEMS

In this paper, the difference between the concepts of the states of a time system introduced in [1] and of the global state sets of general systems introduced in [3] is discussed. A generalization of the concepts of the global state sets and the global systems-response functions of general systems in given. The constructions of the global state sets and the corresponding global systems-response functions of a system are studied. A list of different definitions of dynamical systems is given, from which a few problems are asked, and a new definition of dynamical systems is given, which is a concept based on the mathematical models of general systems and time systems posed in [2, 3].     

Observability of polynomially stable systems

For finite-dimensional systems the Hautus test is a well known and easily checkable condition for observability. Russell and Weiss [A general necessary condition for exact observability, SIAM J. Control Optim. 32 (1994) 1–23] suggested an infinite-dimensional version of the Hautus test, which is necessary for exact infinite-time observability and sufficient for approximate infinite-time observability of exponentially stable systems. In this paper the notion of observability is studied for polynomially stable systems. Several known results for exponentially stable systems are extended to the setting of polynomially stable systems. By means of an example the obtained results are illustrated.     

一类时滞切换系统的输入-状态稳定性分析

利用多Lyapunov函数方法、驻留时间法和Gronwall-Bellman不等式研究了一类时滞切换系统的输入-状态稳定性分析问题．从系统输入-状态稳定定义出发,给出了使得一类时滞切换系统输入-状态稳定的充分条件．与已有的方法相比,无需同时满足构造输入-状态稳定控制Lyapunov函数和所有子系统都是输入-状态稳定的条件,为控制器的设计提供了便利．最后,通过算例仿真验证了所提出方法的可行性．