一类结构不确定采样系统的鲁棒控制

针对一类结构不确定性线性采样系统，在时域中用Lyapunov方法研究采样系统的鲁棒控制及最优鲁棒控制，给出了系统鲁棒稳定的充分条件以及相应的鲁棒控制律，控制律的求取借助于求解一类线性矩阵不等式（LMI），或求解满足特定线性不等式条件下的优化问题，算例结果表明，采样周期是一个关键性的设计参数。     

Robust stability analysis of linear systems with parametric uncertainty

This article is concerned with the problem of robust stability analysis of linear systems with uncertain parameters. By constructing an equivalent system with positive uncertain parameters and using the properties of these parameters, a new stability analysis condition is derived. Due to making use of the properties of uncertain parameters, the new proposed method has potential to give less conservative results than the existing approaches. A numerical example is given to illustrate the effectiveness of the proposed method.     

Robust servomechanism with preview action for polytopic uncertain systems

This paper considers the robust servomechanism design for a polytopic uncertain system subject to a previewable reference signal. Based on the robust mixed LQ/ℋ︁^∞ criterion, we develop a design method of a state feedback controller with integral and preview actions achieving the robust tracking performance in terms of linear matrix inequalities. A numerical example is also included to show the applicability of the present design method. Copyright © 2000 John Wiley & Sons, Ltd.     

On the synthesis of robust PID controllers for plants with structured and unstructured uncertainty

In this paper, we consider the problems of synthesizing PID controllers for robust stability and performance for a given linear time‐invariant plant subject to both parametric and H_∞‐norm‐bounded perturbations. Using results from the area of parametric robust control, synthesis problems are converted into simultaneous stabilization of a family of complex segment polynomials. The results on H_∞ PID synthesis are then used to devise a design procedure for determining the admissible PID gain values. One of the important features of the proposed method is that it constructively characterizes the approximated set of all admissible PID controllers. This characterization can facilitate the optimal design of any additional design requirements. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust controller design for input‐delayed systems using predictive feedback and an uncertainty estimator

This paper deals with the problem of stabilizing a class of input‐delayed systems with (possibly) nonlinear uncertainties by using explicit delay compensation. It is well known that plain predictive schemes lack robustness with respect to uncertain model parameters. In this work, an uncertainty estimator is derived for input‐delay systems and combined with a modified state predictor, which uses current available information of the estimated uncertainties. Furthermore, based on Lyapunov–Krasovskii functionals, a computable criterion to check robust stability of the closed‐loop is developed and cast into a minimization problem constrained to an LMI. Additionally, for a given input delay, an iterative‐LMI algorithm is proposed to design stabilizing tuning parameters. The main results are illustrated and validated using a numerical example with a second‐order dynamic system. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

具有结构不确定性的时滞系统的闭环鲁棒预测控制器

针对具有结构不确定性的时滞系统,设计了闭环鲁棒预测控制算法.该控制算法基于控制不变集方法,通过采用双模控制和闭环控制策略,增加了控制设计的自由度,进而扩大了系统的初始可行域并能获得较优的控制性能.仿真结果验证了该方法的有效性.     

线性不确定中立型时滞系统的鲁棒二次性能

研究具有非匹配条件的范数有界线性不确定中立型时滞系统的稳定和二次性能控制问题．基于Lyapunov方法，提出了系统鲁棒渐近稳定并满足给定二次性能指标的时滞相关型条件，该条件等价干线性矩阵不等式(LMI)可解性问题，并根据LMI的可行解，构造了状态反馈控制器设计方法．     

Robust observer design for uncertain one‐sided Lipschitz systems with disturbances

In this paper, we study the robust observer design problem for a class of uncertain one‐sided Lipschitz systems with disturbances. Not only the system matrices but also the nonlinear functions are assumed to be uncertain. The nominal models of nonlinearities are assumed to satisfy both the one‐sided Lipschitz condition and the quadratically inner‐bounded condition. By utilizing a novel approach, our observer designs are robust against unknown nonlinear uncertainties and system and measurement noises. The new approach also relaxes some conservativeness in related existing results, ie, less conservative observer design conditions are obtained. Furthermore, the problem of designing reduced‐order observers is considered in case the output measurement is not subject to uncertainty and disturbance. Two examples are provided to show the efficiency and advantages of our results over existing works.     

Robust MPC for the constrained system with polytopic uncertainty

An improved method for synthesising the constrained robust model predictive controller is proposed in this study. It constructs a continuum of terminal constraint sets off-line, and achieves robust stability with a variable control horizon on-line from the very beginning and a time-varying terminal constraint set, by solving the min–max optimisation problem, which can be formulated as a linear matrix inequality problem. This algorithm not only dramatically reduces the on-line computation burden, but also guarantees the control performance by reserving at least one free control move in the whole process. Simulation results for the three-tank system with uncertain dynamic behaviour on flux coefficients are given.     

基于状态观测器的多面体不确定随机广义系统鲁棒预测控制

针对It?o型多面体不确定随机广义系统,提出一种离线观测器型鲁棒预测控制器的综合方法.通过构造带有误差项的增广随机Lyapunov函数,运用多维It?o公式和LMI方法,将“min-max”随机规划问题等价转化为一组线性矩阵不等式的求解问题;给出了控制器存在的充分条件和参数表达式,证明了初始时刻的可行解可以保证闭环广义系统的随机容许性.仿真算例验证了该方法的有效性.     

不确定广义系统鲁棒镇定控制器的设计

讨论了线性定常广义系统的稳定性, 给出了这种系统H_∞ 范数形式的稳定性判据, 在此基础上, 利用线性矩阵不等式 (LMI)方法讨论了含有不确定参数的线性广义控制系统的鲁棒镇定问题, 并相应地给出了鲁棒镇定控制器的设计.     

带有状态和输入时滞的不确定广义系统的鲁棒预测控制

针对一类同时具有状态和输入时滞的不确定广义系统, 研究其鲁棒预测控制问题, 给出了鲁棒预测控制器的综合方法. 运用Lyapunov稳定性理论和线性矩阵不等式方法, 近似求解无穷时域二次性能指标优化问题, 从而得到鲁棒预测控制器存在的充分条件和显式表达式. 证明了优化问题在初始时刻的可行解, 可以保证广义闭环时滞系统是渐近稳定且正则无脉冲的. 仿真算例验证了所提出方法的有效性.     

随机不确定系统的鲁棒H∞滤波

研究在同时具有参数和随机不确定的情况下的鲁棒H∞估计问题.假设系统的方程由Ito随机微分方程描述,不确定的参数是范数有界的,外部干扰是随机不确定的.通过解一个线性矩阵不等式,可以设计鲁棒H∞滤波器,最后给出的一个例子对理论分析进行了阐述.     

多输入/多输出系统动态矩阵控制鲁棒稳定性

研究了基于脉冲响应模型的动态矩阵预测控制(DMC)算法,针对多输入、多输出(MIMO)系统脉冲响应模型的特点,利用脉冲响应系数误差矩阵范数平方和定义预测模型的模型误差,以线性矩阵不等式(LMI)的形式提出了DMC闭环鲁棒稳定充要条件,将DMC算法闭环稳定问题转换为一类线性矩阵不等式的可解问题.并且研究了模型误差与闭环系统稳定性之间的关系,给出了保证系统稳定条件下模型误差界的求取方法,通过求解一个线性矩阵不等式约束的凸优化问题得到保证闭环系统稳定的误差界.最后,利用算例对本文方法的有效性进行了验证.     

Event-triggered output feedback control for two-time-scale systems with structured uncertainty

This paper investigates the event-triggered output feedback control problem for the two-time-scale systems with structured uncertainty. Due to the non-ignorable problem in applications such as equipment aging or parameter drifting, the robustness of the designed controller is worth discussing. A dynamic event-triggered scheme is proposed to reduce the computational cost of the control signal. The results indicate that with the proposed event-triggered controller, the system can achieve asymptotic stability without some common restrictions on the fast system rather than practical stability. Moreover, the Zeno behavior is excluded. Simulation examples with comparison studies illustrate the effectiveness of the proposed method.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

一类不确定离散奇异系统的鲁棒稳定化

讨论了离散奇异系统矩阵E中含时不变参数不确定的鲁棒状态反馈稳定化问题.首先,在一系列等价变换下,阐述了其和一个不确定正常线性离散系统的鲁棒状态反馈稳定化问题的等价关系;然后,利用线性矩阵不等式(LMI)方法,给出了鲁棒状态反馈稳定化控制器存在的一个充分必要条件,控制器的设计方法及控制器的一个解;最后,通过一个数值算例验证了本设计方法的有效性.