H∞估计器的LMI设计

本文在Fu等学者研究不确定系统鲁棒H∞估计器的基础上,提出用LMI法设计估计器。指出通常的三个LMI方法求解鲁棒H∞估计器时,存在问题。文中还利用有界实引理,导出待求参数的线性矩阵不等式,还是用LMI法来综合设计鲁棒H∞估计器。     

网络控制系统H∞鲁棒控制器设计

针对存在不确定时延的网络控制系统, 将未知扰动和建模误差转换为满足给定约束的矩阵, 建立具有参数不确定性的网络控制系统模型。基于Lyapunov稳定性理论证明控制系统渐近稳定, 结合线性矩阵不等式完成H∞鲁棒控制器设计。通过仿真实验, 比较在不同时延条件下系统的状态响应曲线, 结果证明所设计的H∞鲁棒控制器可以解决系统中存在不确定建模误差、干扰和时延等问题, 具有一定的鲁棒性。     

基于LMI的H∞鲁棒PID控制器设计

针对一类线性系统,研究了基于H∞的鲁棒PID控制器的设计方法,使得闭环系统的所有极点均位于一个给定的LMI区域中.采用线性矩阵不等式的处理方法,证明了该问题等价于一组线性矩阵不等式的可解性问题.利用该线性矩阵不等式的可行解给出了PID控制器的构造方法,并通过现有的软件Matlab中的工具箱LMI来进行求解.该方法很好地解决了PID控制下的极点指标和H∞鲁棒控制的相容性问题.实际的工程算例验证了该方法的有效性和可行性.     

模糊系统H∞控制器设计的LMI方法

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统H∞控制器的设计问题.首先给出了T-S模糊系统基于状态反馈H∞控制存在的两个新的充分条件.新条件不但简洁而且把模糊子系统间的相互作用表示为由子系统的系数矩阵构成的矩阵不等式.然后新条件被转化为可直接应用Matlab求解的线性矩阵不等式.最后应用线性矩阵不等式方法和Matlab,给出了T-S模糊系统H∞控制器的设计方法.     

H_∞估计器的LMI设计

本文在Fu等学者[1] 研究不确定系统鲁棒H∞ 估计器的基础上 ,提出用LMI法设计估计器。指出通常的三个LMI方法[2 ] 求解鲁棒H∞ 估计器时 ,存在问题。文中还利用有界实引理 ,导出待求参数的线性矩阵不等式 ,还是用LMI法来综合设计鲁棒H∞ 估计器     

基于LMI方法的T-S模糊系统的H∞输出反馈控制器设计

研究了一类T-S模糊系统的H∞控制问题,给出了T-S模糊系统一个新的H∞输出反馈控制器设计方法.该方法充分考虑了模糊子系统间的相互作用.H∞输出反馈控制器可通过求解一组线性矩阵不等式获得.最后通过数值仿真例子,说明所提出的设计方法的可行性.     

不确定时滞系统的鲁棒H∞滤波

对一类同时具有外界干扰和范数有界参数不确定性的时滞系统鲁棒H∞滤波问题进行了研究。对于所有容许的参数不确定性,利用Lyapunov方法,得到以线性矩阵不等式（linear matrix inequality,LMI）表示的鲁棒H∞滤波器设计方法。用该方法设计的滤波器使得滤波误差系统渐近稳定且满足一定的H∞性能指标。给出了滤波器存在的充分条件,并得到了设计滤波器的LMI方法。进而将最优鲁棒H∞滤波器存在的充分条件归结为一个具有线性矩阵不等式（LMI）约束的凸优化问题。最后,仿真结果很好地说明了本文方法的有效性。     

一类不确定性系统鲁棒H∞控制器

研究一类具有匹配不确定性系统鲁棒H∞控制问题,第一,基于矩阵不等式给出了二次稳定的条件并且对系统的H∞性能进行了分析;第二,给出了系统的鲁棒H∞控制器,该控制器不仅满足系统二次稳定的条件,而且也满足H∞性能约束条件;最后,数值算例说明了控制器的有效性和可行性。     

多模型切换系统H∞鲁棒控制器的设计与应用

基于H∞控制理论以及切换系统稳定性理论,对于多输入多输出(MIMO)多模型切换控制系统,提出了一种可以有效抑制抖动和改善瞬态响应性能的鲁棒镇定控制器设计方法.通过引入PI控制思想,根据模型跟踪方法设计了增广状态反馈控制器,并将控制器设计问题转化为方便求解的线性矩阵不等式(LMI).该方法的最大优点是可以很方便的保证多模型切换系统的全局稳定性,同时使得设计的控制器具有较强的鲁棒性.将本文提出的方法应用到某型BTT导弹自动驾驶仪设计中,仿真结果证明了此方法的有效性和优越性.     

一类不确定时滞模糊系统的鲁棒H∞控制

对于一类不确定非线性时滞系统,研究使系统二次稳定的状态反馈控制方法。利用T—S模糊模型对时变时滞不确定非线性系统进行建模,采取分段光滑（PSQ）的Lyapunov函数和线性矩阵不等式方法给出使系统二次稳定的模糊状态反馈控制器存在的充分条件,避免并行补偿法中求解公共矩阵P的困难。仿真试验证明,通过该方法设计的控制器具有良好的鲁棒性,控制效果良好。     

Robust reliable control for a near space vehicle with parametric uncertainties and actuator faults

Based on fuzzy control techniques, this article is concerned with the problem of robust reliable control for a near space vehicle (NSV) with parametric uncertainties and actuator faults. The nonlinear dynamics of a NSV is represented by the Takagi–Sugeno fuzzy models, and then the actuator fault model and fuzzy state-space observer are developed. Next, the fuzzy observer-based robust reliable control strategy is proposed. It is proved that the fuzzy control systems for the NSV is reliable in the sense that the closed-loop system is asymptotically stable and the actuator components can operate well in the presence of some actuator faults. The developed theoretical results are in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Finally, simulation results are given to illustrate the applicability of the proposed approach.     

时变不确定系统鲁棒控制器设计的新方法

基于包含两个二次项的分段Lyapunov函数,研究了线性时变不确定系统的鲁棒控制器设计问题.所考虑的系统由两个矩阵的凸组合构成,通过引入一个附加矩阵,推导出鲁棒控制器存在的充分条件.该控制器的状态反馈增益的求解问题可以转化为一组带有两个比例参数的线性矩阵不等式的凸优化问题.最后的数值示例说明了该设计方法的可行性.     

具有执行器饱和特性的不确定系统预测控制器设计

针对具有执行器饱和特征的不确定系统,提出了一种带有状态观测器的新型预测控制器设计方法.该方法在滚动优化的每一步,采用带有饱和特性的反馈控制结构得到一个最优控制律.使无穷时域性能指标最小.考虑在状态不完全已知的情况下,设计了带有状态观测器的预测控制器,并通过观测器参数调整使闭环系统渐近稳定.通过仿真实验验证了所设计控制器的有效性.     

Linear LMI-based external anti-windup augmentation for stable linear systems

We study linear anti-windup augmentation for linear control systems with saturated linear plants in the special case when the anti-windup compensator can only modify the input and the output of the windup-prone linear controller. We also measure the arising performance in terms of the finite L₂ gain from exogenous inputs to selected performance outputs. Our main results are a system theoretic feasibility characterization for fixed order anti-windup design and a linear matrix inequality (LMI) formulation for optimal static and plant-order anti-windup design. Interpretations of lower bounds on the achievable performance are also given. The effectiveness of the design procedure is demonstrated on a simulation example.     

New dilated LMI characterizations for continuous-time multiobjective controller synthesis

This paper provides new dilated linear matrix inequality (LMI) characterizations for continuous-time controller synthesis. The dilated LMIs enable us to parametrize controllers without involving the Lyapunov variables in the parametrizations. Taking advantage of this feature, we can readily design multiobjective controllers with non-common Lyapunov variables, whereas we are forced to employ a common one in the well-known Lyapunov shaping paradigm. In particular, it is shown that the proposed dilated-LMI-based approach to H₂/D-stability synthesis encompasses the corresponding Lyapunov shaping paradigm as a special case. In this sense, the results of this paper can be viewed as partial counterparts of those obtained in the discrete-time setting.     

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.     

A unified approach to LMI-based reduced order self-scheduling control synthesis

We consider a reduced order controller synthesis for a general class of control specifications for linear parameter-varying (LPV) systems, when some of state variables are exactly available. The class is defined in an abstract manner so that it uniformly deals with many significant specifications. A necessary and sufficient condition for the existence of a reduced order controller is given in terms of linear matrix inequalities (LMIs). We also show that the order of the controller can be reduced by the number of the state variables exactly available in the measurements. Moreover, in the case of linear time invariant (LTI) systems, a parameterization of all desirable reduced order LTI controllers is given by means of solutions of LMIs. The results in this paper generalize the class of control specifications in which a reduced order controller exists, making it possible to synthesize a reduced order controller based on LMIs for multi-objective control specifications. Furthermore, these results uniformly describe and generalize the existing results on synthesis of a constant state and a full order output feedback controller for LTI and LPV systems such that the specification is given by the existence of a constant positive definite matrix.     

Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.