时滞切换系统指数稳定性分析: 微分不等式方法

考虑由多个时滞系统组成的切换系统,并研究在什么条件下,可以把无时滞切换系统的稳定性分析及结论推广至上述的时滞系统.方法是将时滞项作为线性常微分方程扰动项,利用常数变易公式与Halanay微分不等式,分析时滞项对于切换系统稳定性的影响.结论表明,在时滞项满足某些前提时,切换系统稳定性分析的Lyapunov方法仍然适用.仿真算例验证了方法的有效性.     

带有时滞摄动的线性切换系统的稳定性

研究一类带有时滞摄动的线性切换系统的稳定性，分别利用单李亚普诺夫函数方法和多李亚普诺夫函数方法给出了使切换系统渐近稳定的条件和切换律的设计方法。仿真结果验证了所提出设计方法的有效性。     

切换线性时滞系统的稳定性判据

考虑了一类切换线性时滞系统的稳定性问题.基于Lyapunov函数方法和矩阵测度的概念,分别给出了切换系统时滞独立以及时滞依赖的渐近稳定性和指数稳定性判据,设计了相应的镇定切换律.最后,通过数值算例验证了所提算法的正确有效性.     

一类时滞切换系统的稳定性分析

利用时滞分解和平均驻留时间方法讨论一类时滞切换系统的稳定性问题.定义了更为一般的Lyapunov函数,结合Jensen积分不等式和倒数凸组合技术得到的线性矩阵不等式条件具有更小的保守性和更低的计算复杂性给出的仿真算例进一步验证了所得结果的有效性.     

时滞切换不确定神经网络系统的指数稳定性

本文研究了具有无穷时滞切换不确定细胞神经网络(UCNNs)系统任意切换下的指数稳定性.利用同胚映射和M-矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用Lyapunov泛函方法,研究了时滞切换UCNNs系统任意切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.     

基于模糊切换策略的线性切换系统的稳定性

切换系统在运行中常受到干扰、时滞等影响,致使切换系统很难准确实施已确定的切换策略,因此系统的稳定性不能得到保证,鉴于此,本文基于模糊方法研究切换系统的稳定性问题,以增强系统的鲁棒性。将切换系统转换成T—S模糊模型,该系统具有非线性性;依据变量-梯度法,给出此系统在原点的小领域内渐近稳定的充分条件,同时获得模糊切换策略。系统仿真证实此方法简单而有效。     

离散分段线性时滞正系统的稳定性分析

研究了离散的切换线性时滞正系统的稳定性问题．通过运用切换线性余正（copositive）Lyapunov泛函和共同线性余正（copositive）Lyapunov泛函分别得到了关于平衡点全局渐近稳定性的线性规划（LP）和线性矩阵不等式（LMI）判别法则．     

分布参数切换系统的稳定性分析

将切换系统的概念引入到分布参数系统中，提出分布参数切换系统的概念．结合切换系统和分布参数系统的建模方法，建立了两类分布参数切换系统的模型．运用切换系统的稳定性分析方法，对两类分布参数切换系统的稳定性进行分析，得出了指数稳定的充分条件．仿真示例验证了定理的正确性．     

时滞切换系统指数稳定性分析: 多Lyapunov函数方法

将多 Lyapunov 函数方法推广至时滞情形, 分析切换与时滞对于稳定性的影响. 以 Halanay 不等式为引理, 给出了与时滞相关的切换序列约束条件, 以保证系统的指数稳定性. 若时滞项消失, 本文关于切换对于稳定性影响的分析与无时滞情形的相关结论是一致的. 仿真结果说明了本文方法的有效性.     

不确定切换时滞非线性系统状态切换的指数稳定性

利用状态依赖控制策略对切换信号进行设计,使得一类参数不确定时滞非线性切换系统指数稳定且具有一定的??∞抗干扰性能。利用Lyapunov-Krasovskii (LK)函数方法,以线性矩阵不等式组的方式,给出了稳定切换律存在的充分条件,并且该系统是指数稳定的。通过引入自由矩阵并结合积分不等式技巧,得到了保守性较低的稳定性条件。仿真算例表明了所提出方法的有效性和较低的保守性。     

Scheduling Protocols for Switches with Large Envelopes

Traditionally, switches make scheduling decisions on the granularity of a packet. However, this is becoming increasingly difficult since network bandwidth is growing rapidly whereas packet sizes remain largely unchanged. Therefore the service time of an individual packet is decreasing rapidly. In this paper we study switches that make scheduling decisions on the granularity of an envelope which can be much larger than a packet in size. For an output-queued switch with envelope size E, each output chooses one input every E time steps and transmits packets from this chosen input during the next E steps. For an input-queued switch with envelope size E, one matching from the inputs to the outputs is computed every E steps and only the input–output pairs that are defined by this matching are allowed to transmit packets during the next E steps. Traditional switches correspond to envelope size E = 1 and almost all previous scheduling work deals with this case exclusively. We first show how some stable protocols for scheduling networks of output-queued switches with E = 1 fail for arbitrary E when these protocols are generalized in the most straightforward manner. We then present an extremely simple protocol that does guarantee network stability for output-queued switches for any E ≥ 1. For input-queued switches we first present a max-weight matching protocol that is stable for a single switch with arbitrary E. We then present a more complex protocol that achieves stability for a network of input-queued switches for any E ≥ 1.     

二维线性连续系统稳定性的新判据

提出了一个检验二维线性连续系统稳定性的新算法。该算法基于多项式判别系统理论,可以对系统稳定与否作出完备的判断,克服了传统频域方法需要取大量频率点进行检验且只能提供近似结论的不足。更重要的是,此算法可以用于分析含参数系统的稳定裕度。实际案例显示了该算法的有效性。     

Estimation of stability lobe diagrams in milling with continuous learning algorithms

The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). The stability is different for different width of cut and can change with the axis positions. Today it is already a great effort to estimate the SLD only for one position. Many experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only the cutting depth, but also the cutting width should be represented in the SLD. This paper presents a new approach to assess the process stability based on measured acceleration signals. The multidimensional stability lobe diagram (MSLD) are derived during the production using two new continuously learning algorithms. In this paper the application of a continuous learning support vector machine and a continuous neural network is shown. The support vector machine and the neural network are extended to make them capable for continuous learning and time-variant systems. A new trust criterion is introduced, which gives information about the prediction quality of the output for the selected input region. The learned MSLDs are evaluated against analytically calculated MSLDs and the learning algorithms can reproduce the analytical results very well.     

一种确定PID参数稳定域的图解法

针对带滞后因子的一阶惯性环节的PID控制器,给出确定其参数稳定域的一种图解方法．基于参数空间的图解稳定性准则,在已知比例增益范围的前提下,针对稳定和不稳定开环对象,直接在积分-微分参数空间绘制和确定稳定区域,避免了复杂的数学计算．该图解稳定性准则给出闭环稳定的一个充分必要条件,所得结果没有任何保守性．此方法也可用来求解系统的相对稳定度问题和应用于其他任意给定被控对象．     

多项式理论在导弹稳定性能评估中的应用

针对线性参数不确定性系统的鲁棒稳定性问题,提出一种新的分析方法,并对其在导弹自动驾驶仪鲁棒稳定性评估中的可行性进行了研究。首先给出线性参数不确定性系统在其特征多项式系数不相关情况下的鲁棒稳定性的充要条件,并通过自适应网格划分算法将此条件与鲁棒D-稳定性理论结合,得到基于多项式理论的评估算法。将算法用于导弹自动驾驶仪鲁棒稳定性评估,得到了不同攻角下导弹在全包线范围内的稳定区域。和只能在离散点进行评估的传统评估方法比较,结果表明提出的算法可以在全包线范围内连续进行评估,从而发现一些隐蔽的不稳定区域。     

Characterization of robust stability of a class of interconnected systems

We consider robust stability analysis of a class of large scale interconnected systems. The individual subsystems may be different but they are assumed to share a property that characterizes a set of interconnection matrices which lead to stable overall systems. The main contribution of the paper is to show that, for the case where the network interconnection matrix is normal, (robust) stability verification can be simplified to a low complexity problem of checking whether the frequency response of the individual subsystems and the eigenvalues of the interconnection matrix can be mutually separated using a class of quadratic forms. Most interestingly, it is shown that this criterion is also necessary, in the sense that if the criterion is violated, an interconnection matrix of the same eigenvalue distribution can be found to make the overall system unstable.     

Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions

We present a stability criterion for switched nonlinear systems which involves Lie brackets of the individual vector fields but does not require that these vector fields commute. A special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third-order Lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching. This generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed in [D. Liberzon, Lie algebras and stability of switched nonlinear systems, in: V. Blondel, A. Megretski (Eds.), Unsolved Problems in Mathematical Systems and Control Theory, Princeton University Press, NJ, 2004, pp. 203–207.]. To prove the result, we consider an optimal control problem which consists in finding the “most unstable” trajectory for an associated control system, and show that there exists an optimal solution which is bang-bang with a bound on the total number of switches. This property is obtained as a special case of a reachability result by bang-bang controls which is of independent interest. By construction, our criterion also automatically applies to the corresponding relaxed differential inclusion.     

电力电子级联系统稳定性判据研究及仿真验证

独立稳定运行的电力电子装置前后级联运行时,组成的新系统极有可能处于不稳定工作状态,或者不能得到满意的功率转换能效。本文通过对级联系统阻抗比判据的研究,针对前后级不同的阻抗关系,分析级联系统的各类稳定情况,并用仿真实验验证了本文阻抗比判据结果的有效性。     

Comparisons among robust stability criteria for linear systems with affine parameter uncertainties

This paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems, where the system state matrices considered are affinely dependent on the uncertain parameters. At first, a robust stability criterion for the class of systems to be affinely quadratically stable (AQS) is derived based on the vertex separator approach, where affine parameter-dependent Lyapunov functions are exploited to prove stability. Then comparison results between the robust stability criterion and the existing tests for AQS are given in terms of degree of conservatism. A numerical example is given to illustrate the results.     

时滞基因调控网络的全局渐进稳定性分析

针对一类时滞基因调控网络的全局渐进稳定性进行了研究, 利用Lyapunov泛函、线性矩阵不等式（LMIs）和自由权值矩阵（free-weighting matrices）技术, 得到了一些新的时滞相关的基因调控网络稳定性充分条件。通过在Lyapunov泛函中使用辅助矩阵E, 并对调控函数条件一般化, 取得的结果具有较少的保守型和更广的适用性。该结果为人工设计基因芯片提供一定的参考作用。仿真示例进一步验证了结论的有效性。