Delay-dependent Non-fragile H∞ Control for Linear Systems with Interval Time-varying Delay

 This paper considers the problem of delay-dependent non-fragile H_∞ control for a class of linear systems with interval time-varying delay. Based on the direct Lyapunov method, an appropriate Lyapunov-Krasovskii functional (LKF) with triple-integral terms and augment terms is introduced. Then, by using the integral inequalities and convex combination technique, an improved H_∞ performance analysis criterion and non-fragile H_∞ controller are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. At last, two numerical examples are provided to demonstrate the effectiveness of the obtained results.     

Stabilization of Non‐Linear Fractional‐Order Uncertain Systems

In this paper, we present a stabilization method on the non‐linear fractional‐order uncertain systems. Firstly, a sufficient condition for the robust asymptotic stabilization of the non‐linear fractional‐order uncertain system is presented based on direct Lyapunov approach. Secondly, utilising the matrix's singular value decomposition (SVD) method, the systematic robust stabilization design algorithm is then proposed. Finally, two numerical examples are provided to illustrate the efficiency and advantage of the proposed algorithm.     

A Bounded Real Lemma for Discrete‐Time Markovian Jump Singular Systems

This paper presents a bounded real lemma for discrete‐time Markovian jump singular systems. First, a new necessary and sufficient condition is proposed in terms of a strict linear matrix inequality, which guarantees the stochastic admissibility of the unforced Markovian jump singular systems. Then, a bounded real lemma for discrete‐time Markovian jump singular systems is derived. It is also proven that the bounded real lemma can be described by a strict matrix inequality. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory. The results are more tractable and reliable in numerical computations than existing conditions.     

Fractional‐Order Dynamic Output Feedback Sliding Mode Control Design for Robust Stabilization of Uncertain Fractional‐Order Nonlinear Systems

A robust fractional‐order dynamic output feedback sliding mode control (DOF‐SMC) technique is introduced in this paper for uncertain fractional‐order nonlinear systems. The control law consists of two parts: a linear part and a nonlinear part. The former is generated by the fractional‐order dynamics of the controller and the latter is related to the switching control component. The proposed DOF‐SMC ensures the asymptotical stability of the fractional‐order closed‐loop system whilst it is guaranteed that the system states hit the switching manifold in finite time. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.     

Full‐Order and Reduced‐order Observer Design for a Class of Fractional‐order Nonlinear Systems

The paper is concerned with problem of the full‐order and reduced‐order observer design for a class of fractional‐order one‐sided Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full‐order observer error dynamic system is presented. Furthermore, the proposed design method was extended to reduced‐order observer design for fractional‐order nonlinear systems. All the stability conditions are obtained in terms of LMI, which are less conservative than some existing ones. Finally, a numerical example demonstrates the validity of this approach.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.     

不确定奇异系统的变结构控制

针对一类不确定奇异线性系统,利用线性矩阵不等式(LMI)方法获得了滑模运动渐近稳定的充分条件,给出了变结构控制器的设计方法,该方法保证系统状态轨线经有限时间到达滑模面,并在其上实现滑模运动。滑模运动正则、无脉冲模、渐近稳定。     

一类分数阶非线性混沌系统的同步控制

在分数阶非线性系统同步控制的研究中,针对一类分数阶非线性混沌系统,研究了基于分数阶控制器的同步方法.利用状态反馈方法和分数阶微积分定义,设计了分数阶混沌系统同步控制器.进一步,根据分数阶非线性系统稳定性理论、Mittag-Leffler函数、Laplace变换以及Gronwall不等式,证明了同步控制器的有效性.最后,通过数值仿真,实现了初始值不同的两个分数阶非线性混沌系统同步.误差响应曲线表明研究的分数阶非线性系统同步响应速度快,控制精度高,验证了本文所设计的混沌同步控制方案的可行性.     

降阶正实控制器设计

基于线性矩阵不等式 (LMI)方法, 考虑了连续和离散对象的降阶正实控制器设计问题. 通过一阶对象的分析表明, 广义对象阶是最小阶正实控制器阶的可达上界, 因此降阶正实控制器的存在性依赖于具体对象参数. 给出了一个新的降阶正实控制器阶的上界, 该上界蕴涵了已有结果. 上界的估计是构造性的, 可以给出这种降阶正实控制器的设计算法. 文中给出了简单的算例, 说明本文方法的可行性.     

Non-fragile multivariable PID controller design via system augmentation

In this paper, the issue of designing non-fragile H_∞ multivariable proportional-integral-derivative (PID) controllers with derivative filters is investigated. In order to obtain the controller gains, the original system is associated with an extended system such that the PID controller design can be formulated as a static output-feedback control problem. By taking the system augmentation approach, the conditions with slack matrices for solving the non-fragile H_∞ multivariable PID controller gains are established. Based on the results, linear matrix inequality -based iterative algorithms are provided to compute the controller gains. Simulations are conducted to verify the effectiveness of the proposed approaches.     

基于T-S 模糊模型的采样数据网络控制系统H∞ 输出跟踪控制

研究具有采样数据的基于T-S (Takagi-Sugeno) 模糊模型网络控制系统H输出跟踪控制问题. 提出将采集器端数据采样周期、数据传输时滞和数据丢包转换为零阶保持器端数据更新周期, 在此基础上, 利用输入时滞法和PDC (Parallel distributed compensation) 技术, 建立网络环境下被控对象和参考模型合并的基于T-S 模糊模型的增广系统模型. 通过Lyapunov 方法, 并充分利用采样特性, 给出系统实现H输出跟踪的充分条件, 以及可靠模糊控制器的设计. 仿真结果表明所设计模糊控制器能够实现该类系统良好的跟踪.     

不确定线性内互联大系统的分散鲁棒H∞控制

讨论含有界不确定性的线性内互联大系统,通过分散状态反馈和分散动态输出反馈的鲁棒Ｈ∞控制问题,首先给出一个重要引理,然后基于有界实引理分别导出放动态输出反馈的分散鲁棒Ｈ∞控制问题有解的充分必要条件,该条件及其问题的求解等价地转化成一个线性矩阵不等式和双线性矩阵不等式的求解。     

基于混杂系统方法的一类采样数据系统鲁棒故障检测

针对具有连续时间过程噪声和离散时间测量噪声的采样数据系统, 提出了一种新的鲁棒故障检测直接设计方法. 首先利用具有有限跳变的线性系统作为残差产生器, 采样数据系统的鲁棒故障检测设计问题被描述成采样数据滤波问题, 然后给出有限跳变线性系统有界实引理的线性矩阵不等式(LMI)表达形式, 基于此, 推导出采样数据系统鲁棒故障检测滤波器的存在条件及设计参数, 并将所提方法推广到具有结构不确定性的采样数据系统上. 所设计的滤波器能够保证残差与故障之间误差最小, 并对过程噪声、测量噪声、结构不确定性等因素鲁棒. 最后, 通过数值仿真对所提方法的可行性进行了验证.     

奇异摄动系统的鲁棒控制与仿真研究

研究参数不确定奇异摄动系统的状态反馈镇定问题,得到基于线性矩阵不等式（LMI）的系统状态反馈可镇定的充分条件,给出状态反馈控制器的设计算法。算例验证了该方法的可行性与有效性。而且,这种方法同时适用于标准奇异摄动系统和非标准奇异摄动系统的控制。最后通过例子进行了详细的仿真研究。     

时滞T-S模糊系统的无源控制器设计

针对时滞T-S模糊系统, 给出了使得系统无源的状态反馈控制器存在的充分条件, 与现有结果相比保守性更小. 在此基础上, 给出了基于观测器的无源控制器与动态输出反馈无源控制器存在的充分条件. 控制器的设计方法都归结为求解一组线性矩阵不等式(Linear matrix inequality, LMI). 最后通过仿真例子, 说明所给设计方法的有效性.     

不确定关联大系统的最优保成本控制

研究了一类具有数值界不确定性关联大系统的最优分散保成本控制。利用线性矩阵不等式（LMI）,给出了状态反馈最优分散保成本控制律的存在条件,并将最优分散保成本控制器的设计归结为线性矩阵不等式的求解。在求解矩阵不等式的算法上提出了一种迭代LMI算法,该迭代LMI算法引入了同伦算法的思想并结合了此类控制系统自身的特点,同时给出了一种新的权矩阵选择方法。通过迭代LMI算法和选取适当的权矩阵降低了控制器设计的保守性且获得了更优的二次性能指标上界。最后通过数值例子证明了该算法的有效性且具有更小的保守性。     

一类线性时滞系统的鲁棒稳定性分析

针对一类具有范数有界不确定性和2个继发时变时滞的线性时滞不确定系统,研究了其时滞依赖鲁棒稳定性问题.通过定义充分利用时变时滞上下界信息的新型Lyapunov-Krasovskii泛函,并结合时滞系统相关处理方法和线性矩阵不等式方法,得到了时滞线性不确定系统鲁棒渐近稳定所满足的条件.为了降低结论的保守性,对某些项进行了较紧致的估计.此外,并未引入自由权矩阵.最后并通过2个数值仿真证实了方法的有效性和优越性.     

H∞ Model Reduction for Positive Fractional Order Systems

This paper focuses on the H_∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H_∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H_∞‐norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.     

基于二维混合模型的重复控制系统设计新方法

现有重复控制方法是在一维空间上同时处理控制与学习过程, 这不利于重复控制系统的分析与设计. 本文针对一类线性不确定系统, 提出一种基于连续/离散二维混合模型的重复控制系统设计方法. 首先, 通过分析重复控制系统中独立存在的控制行为与学习行为, 建立重复控制系统的连续/离散二维混合模型, 将重复控制器设计问题转化为一类连续/离散二维系统的状态反馈控制问题; 然后应用二维连续/离散系统方法, 获得重复控制系统的稳定性条件, 根据稳定性条件并利用线性矩阵不等式(Linear matrix inequality, LMI)方法, 求得重复控制器参数. 与现有方法相比, 所提出的重复控制设计方法更加符合其本质特征, 具有简单实用、直观明了的特点, 克服了现有重复控制方法所存在的局限性. 最后, 数值仿真实例验证了本文所提方法的有效性.