Inverse Lyapunov Theorem for Linear Time Invariant Fractional Order Systems

This paper investigates the inverse Lyapunov theorem for linear time invariant fractional order systems. It is proved that given any stable linear time invariant fractional order system, there exists a positive definite functional with respect to the system state, and the first order time derivative of that functional is negative definite. A systematic procedure to construct such Lyapunov candidates is provided in terms of some Lyapunov functional equations.     

分数阶动态系统的数值算法

给出了求解分数阶动态系统的一个非常有效的数值方法。本方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。本方法的思想是依据在实际应用中，通常要求给定函数有足够的连续性和光滑性，这就使得它们的Riemann-Liouville和Gruenwald—Letnicov分数导数完全等价。这样在分数阶动态系统中，可以利用Gruenwald—Letnicov分数导数的1阶或高阶近似表达式来近似表示Riemann-Liouville分数导数。最后给出一个仿真实例，说明所给方法的有效性。     

成比例分数阶系统的仿真研究

成比例分数阶系统是一种特殊的分数阶系统.这里提出将成比例分数阶系统的基本阶次项看作一个整体,成比例分数阶系统就转化成一个常规的整数阶系统.通过对成比例分数阶系统的基本阶次项进行近似化研究,减少了系统的复杂性.并用仿真实例进一步演示了该方法的简洁性,可以有效分析成比例分数阶系统问题.     

New Results on Stability and Stabilization of Delayed Caputo Fractional Order Systems with Convex Polytopic Uncertainties

In this paper, the problems of robust stability and stabilization, for the first time, are studied for delayed fractional-order linear systems with convex polytopic uncertainties. The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem. All the results are obtained in terms of linear matrix inequalities that are numerically tractable. The proposed results are quite general and improve those given in the literature since many factors, such as discrete and distributed delays, convex polytopic uncertainties, global stability and stabilizability, are considered. Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.     

基于RBF神经网络的分数阶混沌系统的同步

针对分数阶混沌系统的同步问题,提出一种基于径向基函数(Radial BasisFunction,RBF)神经网络的控制器。利用RBF神经网络对同步误差系统进行补偿控制,神经网络的权值可以在线调整,使得同步误差渐近收敛到零点。基于Lya-punov稳定性理论,分析了该控制器的稳定性。分别以分数阶Chen系统的同步和分数阶Liu系统的同步为例进行了数值仿真,仿真结果验证了所设计的控制器的有效性和鲁棒性。     

时滞相关的多状态时滞系统稳定性分析

对于存在多状态时滞的线性时滞系统,首先将其重新描述为反馈互联系统,利用与时滞相关的有界算子来描述反馈系统的不确定性,并通过人为划分时滞量来减小保守性,基于Lyapunov理论分析稳定性,得到以LMI形式给出的一种保守性小的渐近稳定性条件,结论中能够更加全面的反映系统的状态历史信息,划分越细则保守性越小,实例表明只需粗略划分就能大大提高保守性能,为了兼顾计算负担,r取较小数值即可.并且LMI中的决策变量少,形式简洁.     

STABILITY ANALYSIS FOR THE LARGE-SCALE SYSTEMS WITH TIME-DELAY

The stability analysis problems were put forward for the large-scale systems with time-delayby using the partial decomposition method.With the stability of the isolated subsystems without time-delay,some sufficient criterions for the asymptotical stability of the whole system were obtained bymaking a Lyapunov function with the Razumikhin condition and a Lyapunov functional for the retardedtype and neutral type,respectively.     

系统平均性能测度的稳健估计

研究离散事件仿真中系统平均性能测度θ的估计问题，建立了θ的一种新的估计量—切尾均值．研究表明，这种估计在某些非正态分布中优于传统的估计量—样本均值，并具有稳健性．通过仿真实验对两种估计量进行了评价和比较，并讨论了在正态分布情形中使用切尾均值估计的损失．     

分数阶控制器与整数阶控制器仿真研究

分数阶PID控制器多了两个可调参数,可以取得更好的控制效果.针对位置伺服系统测试问题,设计了分数阶PID控制器,并与整数阶PID控制器相比较,仿真结果演示了分数阶PID制器的控制效果明显优于最好的整数阶PID控制器.无论是在输入发生变化,还是系统负载或参数变化,给出的分数阶PID控制器的控制效果都是比较稳定的.     

线性切换系统的周期性平稳性分析

研究了线性切换系统的周期性和稳定性规律,给出线性切换系统周期性的充要条件及平稳性的充分性判据．为基于混合动态系统Ｐｅｔｒｉ网模型的混合控制器参数验证和设计提供了依据．     

Integrative Stability Analysis for A Class of Intelligent Control Systems

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基于分段模糊Lyapunov函数的模糊系统分析与设计

在分析模糊系统前提规则结构信息的基础上,将模糊Lyapunov函数和分段Lyapunov函数结合,构造出一类连续模糊系统的分段模糊Lyapunov函数。采用并行分配补偿(PDC)结构,利用分段模糊Lyapunov函数进行了稳定性分析与控制律设计,得到了线性矩阵不等式(LMI)形式的连续系统镇定方法。该方法减少了模糊Lyapunov函数与分段Lyapunov函数的局限性,继承两者的优点,所得稳定性判据更为宽松,控制系统具有良好的控制性能。仿真实例表明了该方法的有效性。     

线性离散时滞系统的鲁棒稳定性分析

依据稳定性理论和矩阵范数理论推导了线性离散时滞系统鲁棒稳定的充分条件,在此基础上得到了不确定时滞离散系统扰动矩阵的范数界,根据不确定离散系统的鲁棒D-稳定的定义,给出了确保不确定离散时滞系统所有极点均位于给定圆形区域系统扰动矩阵的范数界,这些条件形式简单,易于实现,是用于初步检验系统稳定性的有用工具.     

Consensus Analysis of Fractional Multi-Agent Systems with Delayed Distributed PI Controller

The consensus problem for fractional multi-agent systems(MASs) with time delay is considered. The distributed fractional proportional-integral(PI)-type controller is designed so that the consensus of the proposed systems is achieved. Moreover, explicit condition to determine the crossing directions is developed. The results show that with the increase of time delay, the closed-loop system has two different dynamic characteristics: From consensus to nonconsensus and consensus switching.Furthermor...     

Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism

In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. Firstly, the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked. Based on this result, a fractional order iteration approach has been developed by modelling the system with fractional order dynamics. Secondly, to reduce the comsumption of computation, a feedb...     

Barrier Lyapunov Function-Based Finite-Time Dynamic Surface Control for Output-Constrained Nonstrict-Feedback Systems

This paper investigates a finite-time tracking problem for the uncertainty nonlinear systems in nonstrict-feedback form, in which the output signal is restricted in a region. Based on the barrier Lyapunov function and dynamic surface control scheme, a novel adaptive neural controller is proposed by using the finite-time Lyapunov technology. Unlike the aforementioned literature on finite time tracking control, the violation of system output constraint is avoided by combining the barrier Lyapunov ...     

Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions

The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilization of uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robust stability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, showing the advanteges of the proposed method.     

广义Delta算子系统稳定性分析

分析广义Delta算子采样周期和稳定域的关系，认为采样周期和稳定域是一个一一对应关系，得出采样周期取值范围可为整个实数轴，稳定域为扩充复平面上的圆域，稳定域的半径为采样周期的倒教。     

Stability Analysis of Nonlinear Measure Large Scale Systems

In this paper,we established the variation of parameters formula of nonlinear large scalesystems containing measures.By means of the lumped Picard iteration method,which avoided thedifficulties of constructing Lyapunov function,we studied the stability,uniform stability,asymptoticstability,uniform asymptotic stability,and exponential stability properties of nonlinear measure largescale systems.