线性时滞系统的耗散控制

从全新的二次型供给率的耗散角度，研究了线性时滞系统的二次稳定性和耗散控制问题，给出了线性矩阵不等式(LMI)形式的充分条件。而且，考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题，同样给出了LMI形式的充分条件，并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。     

Finite-time stabilization via dynamic output feedback

In this paper the finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements.     

中立型时滞系统基于状态观测器的控制设计-LMI方法

研究一类中立型时滞系统基于状态观测器的反馈控制问题。目的是利用线性矩阵不等式(LMI)方法设计状态观测器和动态输出反馈控制器,使得相应的闭环系统渐近稳定。最后给出一个数值例子验证了本文所给结果的有效性。     

An iterative solution to dynamic output stabilization and comments on "dynamic output feedback controller design for fuzzy systems".

In this note, we will show that the output feedback controller gains K in the paper is only an approximated solution K* = QP(-1)C0(dagger), with the dagger denoting Moore-Penrose inverse of the matrix C0. Consequently K is not equal to K* and therefore it may not satisfy the linear matrix inequality (LMI) constraints in the aforementioned paper. Instead, an iterative LMI approach is suggested to solve the dynamic output stabilization problem for the fuzzy systems.     

时变时滞不确定系统的鲁棒输出反馈控制

研究了时变时滞不确定系统基于状态观测器的动态输出反馈实现鲁棒镇定的分 析和综合问题.所研究的系统不仅同时包含时变状态时滞和时变控制时滞,而且包含时变未 知且有界不确定参数.提出了确保该系统可通过输出反馈鲁棒镇定的充分条件,并将该充分 条件转化为线性矩阵不等式(LMI)问题,最终通过求解两个LMI来构造输出反馈控制律.     

基于LMI 的不确定随机系统输出反馈保性能控制

针对一类不确定连续随机系统,研究了具有输出反馈控制器的保性能控制．首先,对于范数有界 的不确定随机系统,得到了具有输出反馈控制器的闭环系统的二次型性能指标的上界一般形式．其次,应用 线性矩阵不等式技术,研究了其闭环系统的二次稳定和二次保性能稳定;并且依据线性矩阵不等式优化方法, 得到了使闭环系统渐近稳定的最优输出反馈保性能控制器．最后,给出仿真算例,验证本文方法的可行性和 有效性．     

Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers

This paper considers the problem of robust H_∞ control for uncertain discrete systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and measured output matrices. Attention is focused on the design of a full-order exponential stable dynamic output feedback controller which guarantees the exponential stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of this problem is presented, which is dependent on the size of the delay. When this LMI is feasible, the explicit expression of the desired output feedback controller is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.     

Delta算子系统动态输出反馈D-稳定鲁棒协方差控制

研究Delta算子描述的线性不确定系统基于动态输出反馈的D-稳定鲁棒协方差控制问题.设计动态输出反馈控制器,使Delta算子不确定系统鲁棒D-稳定,且稳态输出协方差矩阵具有给定上界.利用线性矩阵不等式(LMI)方法,给出D-稳定鲁棒协方差控制器存在的充分条件.在此基础上,提出相应控制器的设计算法.数值算例表明了该设计方法的可行性.     

输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

线性分式不确定系统保成本控制及其鲁棒界

研究线性分式不确定系统的动态输出反馈保成本控制.采用线性矩阵不等式(LMI)方法证明了保成本控制器存在的充分必要条件等价于一个LMI可解性问题,通过该条件将求解闭环系统的成本函数上界的最小值问题转化为一个凸优化问题,利用该凸优化问题的解,得到动态输出反馈控制器的增益矩阵,并且给出了摄动参数允许最大摄动界的一种算法.     

轧辊偏心的H∞输出反馈鲁棒重复控制

针对轧辊偏心问题,用线性矩阵不等式(LMI)方法设计了用于轧辊偏心补偿控制的H∞输出反馈鲁棒重复控制器,首先引入动态输出反馈来保证闭环系统的鲁棒稳定性,把重复控制器设计问题转化为H∞动态反馈控制器的设计问题,采用变量替换法将非线性矩阵不等式转化为线性矩阵不等式并对其求解进而得到控制器参数.另外在采用上述控制器保证系统鲁棒稳定性的同时,通过在重复控制器中引入一个前向系数进一步改善和提高系统的动态性能与稳态控制精度.理论证明与仿真研究表明当系统对象参数存在摄动时,这种控制器仍能有效地补偿轧辊偏心对产品质量的影响.     

线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

Descriptor discrete-time systems with random abrupt changes: stability and stabilisation

This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results.     

线性系统静态输出反馈镇定的LMI方法

利用无约束条件的线性矩阵不等式（LMI）研究了W－问题和P－问题,而后者的解可用来设计静态输出反馈（SOF）镇定控制,作为一个应用考虑了不确定系统的静态输出反馈问题,给出了依赖于LMI条件的SOF设计方法。     

Output feedback decentralized stabilization: ILMI approach

In this paper, the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach. A necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time-invariant large-scale systems. It is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality. The extension of the result to control is studied. An iterative LMI algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain. Examples show the effectiveness of the algorithm.     

Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

In this paper, the problem of asynchronous robust H_∞ dynamic output feedback control for Markovian jump neural networks with norm-bounded parameter uncertainties and mode-dependent time-varying delays is investigated. The improved delay-dependent stochastic stability conditions and bounded real lemma are obtained by introducing the relaxation variables, which reduces the conservatism caused by boundary technology and model transformation. An improved Lyapunov-Krasovskii functional is constructed using linear matrix inequalities. On this basis, the solution of robust H_∞ dynamic output feedback problem and sufficient conditions for solving the problem of asynchronous dynamic output feedback controller are given respectively. Asynchronous dynamic output feedback controller is constructed to ensure that the closed-loop mode-dependent time-varying delays Markovian jump neural networks achieve different convergence speeds. The given H_∞ performance index is satisfied for the delays not bigger than a given upper bound. Numerical examples are employed to show the effectiveness and correctness of the method presented in this paper.

     

不确定系统的鲁棒输出反馈区域极点配置

对一类具有范数有界参数不确定性的线性系统, 研究了使得闭环系统的所有极点均位于一给定圆盘中的输出反馈控制器设计问题. 采用线性矩阵不等式处理方法, 证明了该问题等价于一个线性矩阵不等式的可解性问题, 并利用该线性矩阵不等式的可行解给出了输出反馈控制器的构造方法. 所提出的方法既可应用到连续系统, 也可应用到离散系统.     

脉冲切换系统的鲁棒H∞动态输出反馈控制

考虑了脉冲切换系统的鲁棒H∞控制问题.该系统的状态矩阵和控制矩阵都有不确定性和扰动.利用线性矩阵不等式(LMI)、H∞控制理论、Lyapunov函数和变量替换方法,对这类系统给出了鲁棒稳定且具有γ鲁棒性能的充分条件.然后,使用MATLAB软件设计出H∞鲁棒动态输出反馈控制器和脉冲控制矩阵.最后通过一个仿真算例验证了文中结论的有效性.     

2D system approach based output feedback repetitive control for uncertain discrete-time systems

This paper presents a two-dimensional (2D)-based approach to the problem of output feedback repetitive control for uncertain discrete-time systems. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then sufficient conditions for the existence of output feedback control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal output feedback control law by minimizing the upper bound of a given cost function. Compared with the commonly used 1D-based method, the proposed approach increases the degree of freedom of controller design by not only including in the scheme an output feedback gain but also a feed forward one which can be simultaneously solved using the 2D-based procedures presented in the paper. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Delay-dependent fault detection and diagnosis using B-spline neural networks and nonlinear filters for time-delay stochastic systems

A new fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (PDFs) of the system. The square-root B-spline neural networks is used to formulate the output PDFs with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Delay-dependent criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. It is shown that this new criterion can provide higher sensitivity performance than the existing result. Simulations are given to demonstrate the efficiency of the proposed approach.