LMI优化问题的择一性定理与对偶

考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化...     

Sampled-data nonlinear observer design for chaos synchronization: A Lyapunov-based approach

This paper considers sampled-data based chaos synchronization using observers in the presence of measurement noise for a large class of chaotic systems. We study discretized model of chaotic systems which are perturbed by white noise and employ Lyapunov-like theorems to come up with a simple yet effective observer design. For the choice of observer gain, a suboptimal criterion is obtained in terms of LMI. We present semiglobal as well as global results. The proposed scheme can also be extended for discrete-time chaotic systems. Numerical simulations have been carried out to verify the effectiveness of theoretical results.     

具有离散时滞和分布时滞的中立型时滞系统的鲁棒稳定性

本文研究了具有离散时滞和分布时滞的不确定中立型系统的鲁棒稳定性的问题,考查了可能随时间变化的具有范数有界的不确定性.在对Lyapunov-Krasovskii泛函求导数时,不进行放大估计,而通过引入恰当的零项,构造线性矩阵不等式,从而获得基于LMI的时滞相关稳定的新判据.最后的数值例子说明了所得的结论有效性.     

具有区域极点约束的柔性梁鲁棒H∞振动主动控制

本文基于H∞控制理论研究了传感器和作动器非同位配置情况下,柔性悬臂梁的多模态振动抑制问题。采用频域辨识方法获取低阶名义模型,合理选取加性不确定权函数和性能权函数,将鲁棒H∞控制问题转化为标准H∞控制问题。为了避免H∞控制器设计过程中产生的零极点对消问题,在求解过程中引入区域极点约束。比较了鲁棒H∞控制器和不考虑高阶未建模动态的非鲁棒H∞控制器的控制效果,实验结果表明,设计的鲁棒H∞控制器能够有效抑制柔性梁的前三阶模态振动,而且不会发生溢出问题。     

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.     

Design of controller for Lur’e systems guaranteeing dichotomy

In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman-Yakubovich-Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.     

Observer synthesis method for Lipschitz nonlinear discrete-time systems with time-delay: An LMI approach

In this paper, we address the problem of observer design for a class of Lipschitz nonlinear discrete-time systems with time-delay. The main contribution lies in the use of a new structure of the proposed observer with a novel Lyapunov-Krasovskii functional. Thanks to these designs, new nonrestrictive synthesis conditions, expressed in terms of linear matrix inequalities (LMIs), are obtained. Indeed, the obtained LMIs contain more degree of freedom than those established by the approaches available in the literature which consider a simple Luenberger observer with a simple Lyapunov function for the stability analysis. An extension of the presented result to H_∞ performance analysis is given in order to take into account the noise (if it exists) affecting the considered system.     

线性不确定系统的鲁棒D型迭代学习控制

研究一类线性不确定系统的鲁棒D型迭代学习控制问题.首先针对一类线性标称控制对象,建立其迭代学习控制的二维模型;然后基于获得的二维模型,利用二维系统稳定性理论,获得系统在迭代初态与期望初态一致和不一致两种情形下的D型迭代学习控制律的存在条件和设计方法;进一步,将所得结果推广至控制对象包含不确定性的情形.所得结果以线性矩阵不等式(LMI)的形式给出,可以方便地利用Matlab中的LMI工具箱求解.最后,数值仿真实例验证了本文所提方法的有效性.     

不确定离散模糊随机系统的鲁棒方差约束输出反馈控制

对一类具有范数有界不确定性的离散T-S模糊随机系统。研究不仅使整个闭环模糊系统全局渐近稳定。而且每个模糊子系统的稳态状态方差满足给定上界性能指标约束的输出反馈鲁棒方差控制律的设计问题。利用线性矩阵不等式(LMI)技术，导出输出反馈鲁棒方差控制律的存在条件，并基于矩阵相似变换给出其可解性条件，同时用一组线性矩阵不等式的可行解。给出输出反馈鲁棒方差控制律的一个参数化表达形式。     

Observer-based passive control for uncertain linear systems with delay in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.