On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur ’ e form to guarantee the absolute stability of Lur’ e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.

基于LMI和扰动观测器的电动伺服系统RBF神经网络控制

为了提高电动伺服系统的加载力跟踪精度,基于线性矩阵不等式(LMI)设计扰动观测器和控制器。针对系统中的非线性因素,采用RBF神经网络逼近系统的数学模型;在建立系统跟踪目标模型的基础上,根据LMI设计扰动观测器对控制器进行多余力的补偿,利用李雅普诺夫函数证明扰动观测器和控制器的收敛;在MATLAB/Simulink中搭建仿真模型,分析扰动观测器和RBF神经网络在不同工况下对系统相应量的精准估计,且误差均满足所设定的性能指标,同时与PID控制相比较,证明所提控制策略的控制性能更优。

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

基于LMI的水轮机调节系统扰动观测状态反馈控制策略研究

为进一步提高水轮机的调节性能和控制精度,针对水轮机调节系统提出了一种基于线性矩阵不等式(LMI)的扰动观测状态反馈控制策略。首先,对水轮机调节系统进行了建模,并设计了一种基于LMI的扰动观测状态反馈控制策略,该策略综合考虑了水轮机的运行状态及扰动观测值;然后通过LMI完成了该控制器的设计与分析;最后,为了验证所提控制策略的有效性和鲁棒性,通过仿真试验进行了测试。结果表明,与传统的控制方法相比,该扰动观测状态反馈控制策略可有效提高水轮机调节系统的响应速度、准确性和稳定性,且降低了系统对扰动的敏感性。

Optimal Nonlinear Robust Sliding Mode Control of an Excitation System Based on Mixed Linear H_(2)/H_(∞) Matrix Inequalities

In this paper,an optimal nonlinear robust sliding mode control(ONRSMC)based on mixed H_(2)/H_(∞)linear matrix inequalities(LMIs)is designed for the excitation system in a“one machine-infinite bus system”(OMIBS)to enhance system stability.Initially,the direct feedback linearization method is used to establish a mathematical model of the OMIBS incorporating uncertainties.ONRSMC is then designed for this model,employing the mixed H_(2)/H_(∞)LMIs.The chaos mapping-based adaptive salp swarm algorithm(CASSA)is introduced to fully optimize the parameters of the sliding mode control,ensuring optimal performance under a specified condition.CASSA demonstrates rapid convergence and reduced like-lihood of falling into local optima during optimization.Finally,ONRSMC is obtained through inverse transformation,exhibiting the advantages of simple structure,high reliability,and independence from the accuracy of system models.Four simulation scenarios are employed to validate the effectiveness and robustness of ONRSMC,including mechanical power variation,generator three-phase short circuit,transmission line short circuit,and generator parameter uncertainty.The results indicate that ONRSMC achieves optimal dynamic performance in various operating conditions,facilitating the stable operation of power systems following faults.

基于LMI和BP网络的非线性矩阵加权次优融合算法

为了解决互协方差未知的多传感器非线性系统融合估计问题,提出了一种改进的矩阵加权次优融合算法。利用舒尔补定理推导出线性最小方差意义下基于矩阵融合的最简约束条件。此约束条件可保证融合估计误差方差的正定性,以及所提出次优融合估计的一致性;基于线性矩阵不等式(LMI)提出了一种矩阵加权次优融合估计。考虑到LMI算法优化过程中存在的耗时问题,采用BP网络获取最优值;结合容积卡尔曼滤波算法(CKF),提出了基于LMI算法和BP网络的非线性矩阵加权次优融合算法。仿真分析结果证明了算法应用于非线性系统的有效性。

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks （FCNNs） are special kinds of cellular neural networks （CNNs）. Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality （LMI） approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality （LMI） approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

Solution Building for Arbitrary System of Linear Inequalities in an Explicit Form

The known Fourier-Chernikov algorithm of linear inequality system convolution is complemented with an original procedure of all dependent (redundant) inequalities deletion. The concept of “almost dependent” inequalities is defined and an algorithm for further reducing the system by deletion of these is considered. The concluding algorithm makes it possible to hold actual-time convolution of a general inequality system containing up to 50 variables with the rigorous method of dependent inequalities deletion and up to 100 variables with the approximate method of one. The main application of such an approach consists in solving linear inequality system in an explicit form. These results are illustrated with a series of computer experiments.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

基于LMIs的不确定随机切换系统的H_∞鲁棒控制

基于线性矩阵不等式和控制理论,针对由一组由随机微分方程描述的子系统组成的切换系统,研究此类切换系统在任意切换策略下的鲁棒控制问题,并给出控制器的设计方法。仿真结果表明,所设计的控制器能保证闭环系统在一定意义下的随机稳定。

Experimental Fault Detection in Rotation System Using State Observers by LMIs

Rotating systems have many applications in wide-ranging industrial contexts. The breakdown of this equipment results in economic wastes and leads to dangerous situations. To avoid such problems is very important, and it can be done through tools that inform about the existence of faults, as well as, about their progress in time. A review of the modeling process used for rotor-support-structure shows that the finite element method is the maj or method employed. In this paper, with the aid of well defined theoretical models, obtained using the finite element technique, and the state observer method for the identification and location of faults, it is possible to monitor the parameters of a rotor-support-structure system, including the foundation effects. In order to improve safety, these parameters must be supervised in case of the occurrence of failures or faults. The state observers are designed using Linear Matrix Inequalities （LMIs）. Finally, experimental results （using for this a rotation system in the mechanical vibrations laboratory at Ilha Solteira＇s Mechanical Engineering Department） demonstrate the effectiveness of the methodology developed.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems

The problem of H∞ stability analysis and control synthesis of switched systems with delayed states under arb/trary switchirg laws is considered. By means of Lyapunov function and linear matrix inequality tools, sufficient ctmdition of H∞ stability is presented in terms of linear matrix inequalities. Furthermore, the robust H∞ control synthesis via state feedback and output feedack is studied. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

基于LMI的分段线性系统共存吸引子转迁控制研究

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(linear matrix inequality,LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。基于LMI和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。利用数值方法验证了所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

基于LMI滑模变结构的倒立摆系统稳定控制

以一级倒立摆为研究对象,利用牛顿法建立数学模型,针对其不确定性和稳定性问题,采用指数趋近律,利用线性矩阵不等式方法(LMI)辅助滑模控制策略推导设计出滑模变结构控制器,并结合最优控制理论和饱和函数优化系统参数,提高控制性能。通过Matlab对一级倒立摆系统进行性能仿真验证。仿真结果表明:优化改进后的滑模变结构控制方法在克服系统自身参数的不确定性和外界干扰的同时,有效地抑制了系统抖振,且系统响应快、超调小。

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.