Decentralized H-infinity state feedback control for discrete-time singular large-scale systems

The decentralized H-infinity control problem for discrete-time singular large-scale systems is considered. Based on the bounded real lemma of discrete-time singular systems, a sufficient condition for the existence of decentralized H-infinity controller for discrete-time singular large-scale systems is presented in terms of the solvability to a certain system of linear matrix inequalities by linear matrix inequality (LMI) approach, and the feasible solutions to the system of LMIs provide a parameterized representation of a set of decentralized H-infinity controller. The given example shows the application of the method.     

一类不确定Lurie时滞奇异系统的鲁棒H[[infinity]]滤波

This paper deals with the problem of the robust H1 filtering for a class of Lurie singular systems with state time-delays, parameter uncertainties and unknown statistics characteristics but with limited power disturbance, aiming to design a robustly stable filter such that the uncertain Lurie time-delay singular systems are not only regular, impulse free and stable, but also have a prescribed level of H[[infinity]] performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of linear matrix inequalities (LMIs). When a solution to this set of LMIs exists, the parametric matrices of a desired filter can be easily obtained using LMI toolbox.     

变时滞不确定Lurie系统的时滞分布依赖鲁棒稳定性分析

In this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and normbounded parametric uncertainty is considered. The time delay variation range is divided into two sub-intervals. By considering the probability distribution of the time-varying delay between the two sub-intervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.     

时滞分布参数控制系统指数镇定的LMI方法

A renovating method for distributed parameter control systems with constants, varying-delays, and multi-varying-delays is put forward. By constructing average Lyapunov functions and employing linear matrix inequality (LMI) and other matrix inequality technologies, several sufficient conditions for exponential stabilization are derived. In this method, the conditions are delay-dependent and at the same time, the upper-bound of exponential convergence rate is obtained. In addition, the distinctive advantage of our method is that the criteria mentioned in the paper are easy to check, so it can be applied to practice easily. Finally, a computation example is given to illustrate the proposed method.     

Robust H_∞ Filtering for a Class of Uncertain Lurie Time-delay Singular Systems

This paper deals with the problem of the robust H∞filtering for a class of Lurie singular systems with state time-delays, parameter uncertainties and unknown statistics characteristics but with limited power disturbance,aiming to design a robustly stable filter such that the uncertain Lurie time-delay singular systems are not only regular,impulse free and stable,but also have a prescribed level of H∞performance for the filtering error dynamics for all admissible uncertainties．A sufficient condition for the existence of such a filter is proposed in terms of linear matrix inequalities (LMIs)．When a solution to this set of LMIs exists,the parametric matrices of a desired filter can be easily obtained using LMI toolbox．     

线性多胞型不确定连续系统故障检测滤波器设计

The paper studies the problem of fault detection filter design for uncertain linear continuous-time systems. A design procedure dealing with parameter uncertainties is proposed for residual generation, the sensitivity to fault and the robustness against disturbances are both enhanced on residual outputs through satisfying some performance indexes. By the aid of the generalized Kalman-Yakubovich-Popov (GKYP) lemma, the fault sensitivity performance index can be dealt with in the given frequency range directly, which avoids approximations associated with frequency weights of the existing techniques. An iterative algorithm based on linear matrix inequality (LMI) is given to obtain the solutions. A numerical example is given to illustrate the effectiveness of the proposed methods.     

不确定有损网络控制系统的鲁棒镇定

The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system. Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.     

Guaranteed Cost Control for Discrete-time Singular Large-scale Systems with Parameter Uncertainty

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper.The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model.The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncer- tainties.A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities(LMIs),and a desired state feedback controller is obtained via con- vex optimization.An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

时变不确定切换广义系统的鲁棒最优保性能控制

针对一类时变参数不确定切换广义系统,对其鲁棒最优保性能控制问题进行研究,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件。通过构造广义Lyapunov函数和线性矩阵不等式方法,给出系统鲁棒最优保性能控制器存在的充分条件。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到鲁棒最优保性能控制律及闭环性能指标上界。最后用示例说明该方法的有效性。     

不确定广义系统的保性能控制

针对一类具有范数有界不确定性的连续广义系统和一种具有时间乘积形式的二次性能指标,研究其状态反馈保性能控制器的设计问题.这种性能指标能够使系统状态响应随着时间的增加更快地趋于零,从而缩短系统达到稳定所需要的时间.文中给出了最优保性能控制器存在的充分必要条件并基于双线性矩阵不等式(BMI)、二次矩阵不等式(QMI)和LMI给出其设计方法,最后利用SDP软件和BMI软件举例说明所得结论的可行性.     

基于观测器的广义时滞系统弹性保成本控制

在同时考虑系统矩阵参数不确定性和控制器不确定性对系统性能影响的前提下,研究了一类基于观测器的不确定广义时滞系统的弹性保成本控制问题.基于Lvapunov稳定性理论,通过构造广义Lyapunov函数和广义二次性能指标函数,以线性矩阵不等式的形式给出了基于观测器状态反馈的弹性保成本控制器的设计方法.该控制器不仅保证了广义时滞系统是鲁棒稳定而且使其具有相应的性能指标上界.采用一种新方法将系统弹性保成本控制器设计和状态观测器增益矩阵求取转化为两组严格线性矩阵不等式的可行解问题.最后通过算例验证了该方法的可行性和有效性.     

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．     

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。     

考虑执行机构故障的离散系统可靠保性能控制设计

对一类离散时间线性时不变系统,研究当执行机构发生连续增益故障情况下的可靠保性能状态反馈控制律的设计问题.应用线性矩阵不等式处理方法,导出系统存在可靠保性能控制律的一个充分条件,进而用一个线性矩阵不等式的可行解给出所有可靠保性能控制律的一个参数化表示.在此基础上,通过建立和求解由一组线性矩阵不等式所表示的凸优化问题,得到最优可靠保性能控制律的设计方法.     

一类线性切换广义系统的保性能控制

针对一类线性切换广义系统,研究了其在任意切换策略下的保性能控制问题。结合一个二次型性能指标,利用单Lyapunov函数方法和线性矩阵不等式(LMI)技术,给出了状态反馈保性能控制器存在的一个充分条件,使得相应的闭环切换广义系统保持正则、稳定和无脉冲,且闭环性能指标值不超过某个确定上界。并进一步将保性能控制器的设计问题转化为线性矩阵不等式的可行解问题,使得控制器的设计更加简便,易于操作。这个条件可以通过Matlab的LMI工具箱求解,适合在工程中应用。数值仿真例子说明了该方法的有效性。     

约束条件下不确定系统的保性能控制

针对一类范数有界不确定连续时间系统，研究在控制输入存在位置约束条件下的状态反馈保性能控制问题。给出约束条件下保性能控制律存在的充分条件，并等价为线性矩阵不等式的求解问题。给出控制器的参数化表示。通过数值仿真验证所得结论的正确性。     

一类不确定离散非线性时滞系统保性能控制

针对状态不完全可测的一类不确定连续离散时间非线性系统,基于状态观测器研究其保性能控制问题。采用T-S模型对非线性系统进行建模,根据李雅普诺夫稳定性理论,基于线性矩阵不等式(LMI),利用分散化并行分布补偿(PDC)的方法设计了基于观测器的控制器,给出了实现该非线性系统保性能控制的充分条件。在此基础上通过求解相应的线性矩阵不等式组给出了控制器和观测器的设计方法,并通过数值仿真验证了提出的方法,仿真结果表明该方法是正确的。