Estimate of total stability of delay difference systems

The concepts of total stability and total asymptotic stability for delay difference systems in the general form are defined. Moreover, the criteria for total stability and total asymptotic stability of linear delay difference systems are established. The obtained results are qualitative and quantitative in the sense that the estimates of the total stability region and the total asymptotic stability region are given.     

On the gait stability of biped machines

The control and stability properties of legged machines in locomotion are considered. The general stability of all such machines is separated into three categories: stability of the body's orientation with respect to earth; stability of the body's trajectory; stability of the gait. The control laws for a fully dynamic system with six degrees of freedom are presented. Their stability properties are studied by simulation with the introduction of disturbances.     

Novel development of Lyapunov stability of motion

The paper presents a refined analysis of the influence of initial data on dynamic behaviour and stability properties of non-stationary systems. As a result, new stability properties are discovered and defined as well as the corresponding stability domains. Furthermore, general necessary conditions are established for asymptotic stability of the unperturbed motion of these systems, the instantaneous asymptotic stability domain of which can be either time-invariant or time-varying and then possibly asymptotically contractive. It is shown that the classical Lyapunov stability conditions cannot be applied to the stability test as soon as the system instantaneous domain of asymptotic stability is asymptotically contractive. In order to investigate asymptotic stability of the motion in such cases novel criteria are established. Under the criteria the Eulerian derivative of a system Lyapunov function may be non-positive only and still guarantee asymptotic stability of the unperturbed motion

The results are illustrated by examples.     

Stability analysis of Runge–Kutta methods for differential equations with piecewise continuous arguments of mixed type

This paper deals with the stability analysis of the Runge–Kutta methods for a differential equation with piecewise continuous arguments of mixed type. The stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical experiments are given.     

基于不变集的一类混合系统的稳定性

利用混合Ｐｅｔｒｉ网为混合系统建模,探讨了基于不变集混合系统在Ｌｙａｐｕｎｏｖ意义下关于恢复半径的稳定性概念,并给出利用Ｌｙａｐｕｎｏｖ函数法判定混合系统稳定性、一致稳定和渐近稳定的充分条件。     

Stochastic stability properties of jump linear systems

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for δ-moment stability is monotonically converging to the region for almost sure stability at δ↓0⁺     

New stability criterion for a class of uncertain nonlinear neutral time-delay systems

In this paper, asymptotic stability for a class of uncertain nonlinear neutral systems with a single time delay is considered. A new delay-dependent criterion is proposed to guarantee stability for such systems. The Lyapunov stability theorem and matrix inequalities are used to prove the main result. Finally, four numerical examples are given to demonstrate that our robust stability condition is less conservative than those reported in the control literature. The tolerable time-delay intervals that guarantee asymptotic stability of systems are larger than other results in those examples.     

On asymptotic stability of linear neutral delay-differential systems

The stability testing problem for linear neutral delay-differential systems is addressed. By means of the concept of spectral radius, both delay-independent and-dependent stability criteria are derived. These criteria are also extended to the neutral systems with multiple time delays. The main results proposed here are better than those reported in the literature. Compared with the several existing stability criteria, the stability robustness bounds are significantly improved. Some examples are used to show the significance of our results.     

Globally asymptotical stability of discrete-time analog neuralnetworks

Some globally asymptotical stability criteria for the equilibrium states of a general class of discrete-time dynamic neural networks with continuous states are presented using a diagonal Lyapunov function approach. The neural networks are assumed to have the asymmetrical weight matrices throughout the paper. The resulting criteria are described by the diagonal stability of some matrices associated with the network parameters. Some novel stability conditions represented by either the existence of the positive diagonal solutions of the Lyapunov equations or some inequalities are given. Using the equivalence between the diagonal stability and the Schur stability for a nonnegative matrix, some simplified global stability conditions are also presented. Finally, some examples are provided for demonstrating the effectiveness of the global stability conditions presented.     

Stability analysis of discrete-time adaptive control schemes

The stability properties of a fairly general diserete-time adaptive control scheme are analyzed. Sufficient conditions forL^{infty}stability in the presence of disturbances are given. The stability results are used to prove convergence of the process outputs in the disturbance-free case, without requiring any a priori stability assumption.     

Uniform stability of discrete impulsive systems

This article studies discrete impulsive systems. The uniform stability (uniformly asymptotic stability and quasi-exponential stability) criteria are established for linear discrete impulsive system and a class of nonlinear discrete impulsive systems, respectively. These stability criteria are expressed in terms of fairly simple algebraic conditions so that they are easy to be tested. Moreover, by using the stability criteria, a discrete impulsive synchronization scheme is designed to synchronize two discrete chaotic systems. Finally, some examples are given to illustrate results obtained by us.     

宏观经济系统的稳定性

首先研究固定资产投资的稳定性，然后在此基础上研究宏观经济系统的稳定性问题，并得到了宏观经济系统稳定、渐近稳定和不稳定的充分条件     

Stability conditions for the sequential design of non-diagonal multivariable feedback controllers

Sufficient conditions to guarantee closed-loop internal stability for sequentially designed multivariable feedback control systems are developed in this paper. The class of MIMO systems considered have transfer function matrices that are square and invertible. The contributions of these stability conditions to the knowledge base of sequential loop design are two-fold. First, unstable Smith-McMillan pole-zero cancellations in the feedback loop are explicitly considered, thus ensuring internal closed-loop stability. Second, the class of systems addressed is expanded to include MIMO systems with non-minimum phase Smith-McMillan zeros. An important feature of the proposed stability conditions is that the elements of the controller matrix which must be non-zero to achieve internal stability are transparently displayed. As a result, only those off-diagonal controllers needed to achieve the pre-specified stability objectives are used, thus reducing implementation complexity. The application of the stability criteria is demonstrated in a design example for an unstable, non-minimum phase (2 2 2) system.     

Equations of perturbed motions and stability of state and semi-state systems

Problems in the construction of equations of perturbed motions for state and semi-state systems are discussed. It is shown that in most cases it is not possible to construct the equations of the perturbed motions, so that the classical approach to the stability analysis of a selected motion is not applicable. The necessary and sufficient stability conditions that provide the testing of stability of an arbitrary system motion, without the utilization of the equations of perturbed motions, are developed. The results obtained concern the original Lyapunov stability definition and contain as special cases some other existing stability results. Two examples are worked out: one of them concerns the analysis of a non-linear feedback system that does not possess a state model.     

Stability of matrix second-order systems: new conditions andperspectives

Modeling of many dynamic systems results in matrix second-order differential equations. In the paper, the stability issues of matrix second-order dynamical systems are discussed. In the literature, only sufficient conditions of stability and/or instability for a system in matrix second-order form are available. In this paper, necessary and sufficient conditions of asymptotic stability for time-invariant systems in matrix second-order form under different types of dynamic loadings (conservative/nonconservative) are derived and a physical interpretation is carried out. The stability conditions in the sense of Lyapunov (the jw-axis behavior of eigenvalues) are also analyzed. As the conditions are gained directly in terms of physical parameters of the system, the effect of different loadings on the system stability is made transparent by dealing with the stability issues directly in matrix second-order form     

Frequency criteria for bounded-input--Bounded-output stability of nonlinear sampled-data systems

Sufficient conditions for absolute stability in the bounded-input-bounded-output sense are obtained for a class of nonlinear sampled-data systems. The criteria are identical to those establishing absolute stability in a global stability sense for the same class of autonomous nonlinear sampled-data systems.     

一类缺乏明确平衡点的不确定系统的部分变量镇定

针对一类缺乏明确平衡点的不确定系统,研究了系统部分变量的稳定性问题. 提出了将一致最终有界和渐近稳定相结合的系统稳定性模式,并给出了该系统稳定性模式的条件. 基于该稳定性模式,提出了阻尼配置控制方案,使系统部分变量在不同阶段稳定于给定运行区域和原点. 所开展的研究工作拓展了不确定系统的稳定性研究,解决了工业应用中普遍存在的一类缺乏明确平衡点的不确定系统的部分变量控制问题. 永磁同步电机的仿真验证了研究结果的有效性和实用性.     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

On the stability of multiloop feedback systems

Some extensions on recent work in passive stability theory by Desoer and the author are presented. The stability of feedback systems is considered where the forward-loop and return-loop subsystems each have been subdivided into several systems operating in parallel. Results are obtained in the areas of Lyapunov stability, L2input L2output stability, and bounded-input bounded-state stability. Before applying these results to a specific multiloop feedback system, a pseudoenergy analysis must be done on each sub sub-system. Two specific types of systems are so analyzed. The first is a general linear first-order time-varying system. The second is a linear time-varying infinite-dimensional system; the analysis of this system takes the form of a Kalman-Yacubovich-type lemma. By using these two new systems, along with several others that have been analyzed previously, stability theorems for many specific multiloop feedback systems can be proven. One such example is given.     

Stability investigation of the sign representation of images

The stability notion of the sign representation of images is introduced. Group properties of the invariant transformations on sign representations of images are investigated. Analytical estimates are obtained of the stability measure of the sign representation of images noise-affected by the normal additive noise. The relation is set up between the stability of the complete sign representation and the stability of the window sign representation. The results of the statistical modeling that confirm the validity of theoretical estimates are presented.