分数阶线性系统的内部和外部稳定性研究

介绍了分数阶线性定常系统的状态方程描述和传递函数描述．运用拉普拉斯变换和留数定理，给出并证明了分数阶线性定常系统的内部和外部稳定性条件，并讨论了其相互关系．以一个粘弹性系统的实例验证了上述方法的正确性．     

灰色系统稳定性充分条件及其在线性时变系统稳定性分析中的应用

本文利用非负不可约矩阵的性质分析了灰色线性定常系统的稳定性问题,给出了灰色线性定常系统稳定性充分判据。所得判据不仅可用来分析灰色线性定常系统的稳定性,而且可用来分析线性时变系统的稳定性。作为所得判据的应用实例,本文还给出了确保线性时变系统稳定的充分条件。借此,可使很大一类线性时变系统的稳定性判定问题变得十分简单。     

分数阶线性定常系统的状态反馈镇定

研究了在分数阶受控系统中稳定性的问题。假定分数阶系统是在线性定常的情况下,利用状态反馈的方法,构造状态反馈矩阵以实现对系统的稳定性控制;给出了分数阶系统由状态反馈镇定的条件及其证明,并给出了状态反馈镇定的综合算法。仿真实例证明了采用状态反馈实现系统镇定的可行性和有效性。     

分数阶系统状态空间描述的数值算法

利用Grünwald-Letnicov分数微积分定义计算分数微积分的数值解,计算精度仅为1阶,不能满足快速收敛性要求.给出并证明了分数阶微积分的高阶近似所应满足的条件,并在此基础上推导出分数阶线性定常系统状态空间描述的数值计算公式.本法不但公式简单易编程,而且具有计算精度高、运算速度快等优点.给出一个粘弹性动态系统的仿真实例,验证了其有效性.     

线性定常时滞系统全时滞渐近稳定的充分代数判据

本文探讨了线性定常时滞系统全时滞渐近稳定性问题,并给出了简单实用的稳定性充分 代数判据.     

一种有效的不确定分数阶T-S模糊系统的控制器设计方法

考虑分数阶非线性系统的稳定和镇定问题,基于线性矩阵不等式(LMI)方法,对分数阶T-S模糊系统进行研究.利用并行分布补偿法,设计分数阶T-S模糊系统的控制器.考虑阶次满足$0<\alpha<1$的分数阶系统,给出可以利用Matlab求解的LMI形式的T-S模糊控制器设计镇定判据.该判据的优点是可以处理具有正实部特征根的分数阶T-S模糊系统的稳定性和镇定问题,能够保持与Matignon分数阶系统稳定性结论的一致性,并克服其他方法只能处理特征根在负实部的方法的局限性和保守性.数值仿真结果验证了所提控制器设计方法的有效性.     

分数阶控制系统

随着基于分数阶次的数学理论日益完善,分数阶控制系统也越来越广泛地被研究和讨论。为了完善分数阶控制系统的理论体系,给出了分数阶系统的总体综述。介绍了分数微积分的定义,给出了分数阶线性定常系统的传递函数和状态空间描述,简要介绍了分数阶控制系统的复频域分析和分数阶控制器及控制器的设计方法,并分析了几种设计方法的优缺点。分数系统的研究必然能找到合适的切入点广泛地进入现代控制领域,为真正实现工业控制自动化提供强有力的理论依据。     

分数阶系统的动力性质及反馈控制

利用一元连续函数的介值定理和Gerschgorim圆盘定理,分别给出了分数阶系统混沌性和稳定性的一个充分判据.应用该判据,可以对所有的分数阶混沌系统进行反馈控制.最后将此理论应用于文献[12]新提出的分数阶混沌金融系统,仿真结果验证了此理论的正确性.     

不确定广义系统鲁棒镇定控制器的设计

讨论了线性定常广义系统的稳定性, 给出了这种系统H_∞ 范数形式的稳定性判据, 在此基础上, 利用线性矩阵不等式 (LMI)方法讨论了含有不确定参数的线性广义控制系统的鲁棒镇定问题, 并相应地给出了鲁棒镇定控制器的设计.     

一种实用的递推稳定判别法

判别线性定常连续系统的稳定性,是我们在实际工作中经常遇到的问题。一般常用劳斯判据作为工具,然而,劳斯判据的计算量比较大,系统的阶次稍高时,计算就显得非常麻烦。因此,希望找到一种能够很方便地对系统稳定性进行判别的简单办法。本文基于苏联学者近年证明的一些重要结论,给出了一种判别稳定性的递推算法,并给出了计算器上用的程序,应用起来极为方便。     

Stability analysis of neural-network interconnected systems

This paper is concerned with the stability problem of a neural-network (NN) interconnected system which consists of a set of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Subsequently, based on the LDI state-space representation, a stability criterion in terms of Lyapunov's direct method is derived to guarantee the asymptotic stability of NN interconnected systems. Finally, a numerical example with simulations is given to demonstrate the results.     

Stability robustness analysis of digital control systems in state-space models

The stability robustness of discrete linear time-invariant systems in state-space models is analysed. Based on a root-locus approach and from the stable-eigenvalue viewpoint, fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems. Both the norm bound and the element bounds for the allowed perturbations are obtained. A stability robustness index is denned which is useful both for the analysis and synthesis of control systems.     

On the asymptotic stability of the null solution of linear differential equations with periodic coefficients

A stability criterion for feedback systems with a linear time-invariant forward loop and a periodically time-varying gain in the feedback loop is developed. As most recent frequency-domain stability criteria, it requires the existence of a multiplier having certain properties. A graphic technique is given to determine whether or not this multiplier exists. The proof of the criterion is based on the Floquet theory and the classical theory of Toeplitz forms. Examples to illustrate the criterion are included.     

The relationship between minimum entropy control and risk-sensitivecontrol for time-varying systems

The connection between minimum entropy control and risk-sensitive control for linear time-varying systems is investigated. For time-invariant systems, the entropy functional and the linear exponential quadratic Gaussian cost are the same. In this paper, it is shown that this is not true for general time varying systems. It does hold, however, when the system admits a state-space representation     

Robust stability and robust pole assignment of linear systems withstructured uncertainty

Sufficient conditions for the robust stability of linear time-varying systems are presented. The stability criteria are extended to the problem of the robust pole assignment of linear time-invariant systems to a specified region. These criteria, both for robust stability and robust pole assignment, improve some results in the literature. Examples are given to demonstrate the new criteria     

A general algorithm for determining state-space representations

A new and direct procedure is presented for determining state-space representations of given, time-invariant systems whose dynamical behavior is expressed in a more general, differential operator form. The procedure employs some preliminary polynomial matrix operations, if necessary, in order to “reduce” the given system to an equivalent differential operator form which satisfies four specific conditions. An equivalent state-space representation is then determined in a most direct manner; i.e. the algorithm presented requires only a single matrix inversion. An explicit relationship between the partial state and input of the given system and the state of the equivalent state-space system is also obtained.     

Lyapunov stability of n-D strongly autonomous systems

In this article we look into stability properties of strongly autonomous n-D systems, i.e. systems having finite-dimensional behaviour. These systems are known to have a first-order representation akin to 1-D state-space representation; we consider our systems to be already in this form throughout. We first define restriction of an n-D system to a 1-D subspace. Using this we define stability with respect to a given half-line, and then stability with respect to collections of such half-lines: proper cones. Then we show how stability with respect to a half-line, for the strongly autonomous case, reduces to a linear combination of the state representation matrices being Hurwitz. We first relate the eigenvalues of this linear combination with those of the individual matrices. With this we give an equivalent geometric criterion in terms of the real part of the characteristic variety of the system for half-line stability. Then we extend this geometric criterion to the case of stability with respect to a proper cone. Finally, we look into a Lyapunov theory of stability with respect to a proper cone for strongly autonomous systems. Each non-zero vector in the given proper cone gives rise to a linear combination of the system matrices. Each of these linear combinations gives a corresponding Lyapunov inequality. We show that the system is stable with respect to the proper cone if and only if there exists a common solution to all of these Lyapunov inequalities.     

一类多输入多输出网络控制系统的稳定性分析

研究了具有分布时延、有界输入的多输入多输出网络控制系统的建模和稳定性问题.基于线性时不变对象,建立了系统的数学模型.利用李雅普诺夫第2方法和线性矩阵不等式描述,分析了系统的渐近稳定性,导出了与时延相关的系统渐近稳定判据,同时得到了系统稳定运行的最大允许时延.系统渐近稳定的最大允许时延可用MatlabLMI工具箱从稳定判据获得.仿真算例表明稳定判据是可行的.