Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Discrete Fractional Lagrange Equations of Nonconservative Systems

In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.

Leader-following consensus of discrete-time fractional-order multi-agent systems

Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.

The identification algorithm for commensurate order linear time-invariant fractional systems

An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

Identification algorithm for a kind of fractional order system

The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.

Digital implementation of fractional order PID controller and its application

A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.

分数阶(2+1)维Hybrid-Lattice系统的精确解

将G′/G展开法应用到离散分数阶系统,成功求解了分数阶(2+1)维Hybrid-Lattice系统的精确解。研究结果显示,利用该方法求解分数阶(2+1)维Hybrid-Lattice系统十分简洁高效。

中国旱地系统地表植被-土壤状态演化路径识别与过程分析

旱地系统作为典型的脆弱生态系统,其地表状态的非线性演化深刻影响着生态平衡与人类福祉,但现有研究尚未全面揭示其复杂的动态演化过程。本文基于2001—2022年逐月植被和土壤地表要素丰度值时间序列产品,采用基于离散小波变换的趋势和转折点检测算法,识别旱地系统植被-土壤状态演化路径并分析其动态变化。结果表明:①2001—2022年,中国旱地系统光合植被和非光合植被端元丰度值都呈显著增加趋势,而土壤生境端元丰度值呈显著减少趋势;②光合植被突然上升、A形上升和V形上升的状态演化路径类型分别占旱地总面积的9.9%、16.8%和21.9%,而非光合植被对应的3种状态演化路径则分别占9.1%、12.6%和28.8%;③整体上旱区的植被恢复促进了土壤裸露的减少,但局部地区水资源匮乏和人类活动导致植被退化。本文为理解中国旱地系统的地表状态演化及其响应机制提供了新视角,并为土地退化监测与生态修复提供了科学依据。

二维分数阶卡尔曼滤波及其在图像处理中的应用

该文研究了二维分数阶卡尔曼滤波及其在图像增强与滤波中的应用问题。首先基于分数微积分的定义,建立了二维线性离散系统的分数阶差分状态空间模型。然后,提出了一种可应用于图像信息处理的二维分数阶卡尔曼滤波算法,并通过实验验证了该文提出算法的有效性。仿真结果证明,该算法增强了图像中的细节特征,同时消弱了图像中的背景噪声。

离散时间分数阶多自主体系统的时延一致性

复杂工作环境中,许多自然现象的个体动力学特性用整数阶方程不能描述,只能用非整数阶(分数阶)动力学来描述个体的运动行为.本文假设多自主体系统内部连接组成有向加权网络,个体的动态特性应用分数阶动力学方程描述,个体之间数据传输存在通信时延.应用分数阶系统的Laplace变换和频域理论,研究了离散时间的分数阶多自主体系统的渐近一致性.应用Hermit-Biehler定理,研究了具有样本时延的分数阶多自主体系统的运动一致性,得到保证系统稳定的时延的上界阈值.最后应用一个实例对结论进行了验证.

基于分数阶超混沌系统和DWT的数字水印研究

为了提高基于低维整数阶混沌系统的数字水印的加密效果,提出了采用分数阶超混沌系统对数字水印图像进行加密,并通过离散小波变换对密文水印进行嵌入及提取的方法。首先,借助预估-校正法产生分数阶Liu超混沌系统的混沌序列,并利用混沌序列对明文水印图像进行混沌置乱和像素值扩散加密;然后,运用离散小波变换对宿主图像和密文水印图像进行分解和重构,实现密文水印的嵌入和提取;最后,对水印加密系统的初值和分数阶阶数敏感性进行验证,并且对含水印图像进行像素损毁攻击和JPEG压缩攻击测试。实验表明,基于分数阶超混沌系统和DWT的数字水印方法在加密解密、抗像素损毁攻击和抗JPEG压缩攻击等性能方面具有良好的效果。

基于超混沌系统和离散分数随机变换的图像加密算法

本文结合超混沌系统和离散分数随机变换,提出一种图像加密新方案,并给出实现该算法的光学装置原理图。在加密过程中,利用超混沌系统产生的混沌序列来构造离散分数随机变换(DFRT)的随机矩阵,再将DFRT的阶数和超混沌系统的初始值作为图像加密算法的主密钥,与单纯的离散分数随机变换的图像加密算法相比,在不增加计算负担的情况下,本算法的明文与密文之间具有更高的复杂性,并加大了密钥空间,提高了密钥敏感性。该系统是一个非线性的密码系统,消除了传统加密系统中因为线性过程而存在的不安全因素,提高了加密系统的抗统计攻击和噪声攻击的能力。

分数阶离散Lorenz系统的动力学行为

研究了一个分数阶离散Lorenz映射系统的动力学行为.首先研究了系统随不同参数变化的动力学行为,发现系统发生了周期倍分岔和Hopf分岔.然后为了进一步研究系统的动力学行为,基于数值模拟,得到了系统随参数和分数阶的阶数同时变化的三维分岔图.通过三维分岔图发现,该映射系统随着阶数的逐渐减小,动力学行为变得越来越简单,最后完全进入周期窗口;随着阶数逐渐增大,动力学行为变得越来越复杂.

带有混合时滞的分数阶非线性系统稳定性研究

研究了一个带有离散时滞和分布时滞的分数阶非线性混合时滞系统的渐近稳定问题。根据Lyapunov间接法,结合Riemann-Liouville型积分算子的连续频域分布模型和Lyapunov-Krasovskii方程,构造了一个全新的Lyapunov函数,给出分数阶非线性混合时滞系统的渐近稳定条件,并根据所给的稳定条件设计了一个反馈控制器,最后通过算例仿真验证判定条件的可行性。

分数阶控制器的一种IIR型滤波器近似算法

从滤波器的角度,采用IIR型滤波器对控制信号进行分数阶近似运算,详细介绍了由Simp-son积分算法和Tustin积分算法插值倒置后得到的二阶滤波器算法,并给出仿真实例验证其有效性。

稳态分数阶Kalman滤波器

基于CARMA新息模型对线性离散分数阶状态空间系统提出一种稳态分数阶Kalman滤波器。分数阶描述比整数阶描述更精确,所提出的滤波器相比已有的整数阶系统的相关研究结果更具普遍性和实用性。仿真实例表明了该滤波器的有效性。

时滞系统基于离散GM(1,2,τ_d)模型的新型控制算法

本文采用系统的输出反馈 ,通过引进趋近律 ,提出了一种基于离散GM ( 1,2 ,τd)模型的分数时滞系统的滑模控制 (SMC)算法。在设计控制器时 ,仅仅利用了系统的输出反馈而非系统的状态反馈 ,故该算法既实用 ,又易于实现。

混沌系统耦合2D离散分数随机变换的双图像同步加密算法研究

当前图像加密算法都具有较高的安全性,但是,这些只能对单幅图像完成扩散,无法同步加密多个图像。而现有的多图像加密主要是借助信息压缩思想,将多个图像压缩成单图像,继而完成加密。然而,这种压缩技术易丢失图像信息,造成较大失真。为此,设计了混沌系统耦合2D离散分数随机变换的双图像同步加密算法。首先,利用Chen’s系统生成混沌序列,构造置乱引擎,对其中一个图像完成扰乱,并将该置乱图像编码成相矩阵;再联合相矩阵与另外一幅明文图像,形成复杂矩阵;最后,迭代Logistic映射,生成随机矢量,设计对称随机矩阵,嵌入2D离散分数随机变换中,基于复杂矩阵,构造双图像并行加密机制,完成图像像素扩散。实验数据显示:其图像加密算法能同时多两幅图像完成加密,拥有较高的安全性;且算法的失真度较小,较好地保留了明文图像信息。