Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Robust H_∞ static output feedback control of discrete-time switched polytopic linear systems with average dwell-time

This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler＇s lemma and Dualization lemma, some novel conditions for exponential H∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities （LMIs）, which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.

Optimal Guaranteed Cost Control via Static Output Fedback for Uncertain Discrete-Time Systems

目的研究在状态空间模型中的状态及控制矩阵中含有范数有界参数不确定线性离散系统的最优保价静态输出反馈控制问题．方法给出了系统二次代价指标的一个上界，并利用拉格朗日乘子法优化了该界．结果与结论给出了保证闭环系统二次稳定且使得二次代价指标界达到最小的静态输出反馈控制器存在的充分条件．并提供了一个求解输出反馈增益的数值算法．

Output Feedback Controller Design for Discrete-time Switched Singular Systems

This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.

Quantizer design for interconnected feedback control systems

In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-infinity disturbance attenuation level is achieved, and that the subsystems＇ measurement outputs are quantized before they are passed to the local controller. We propose a local-output-dependent strategy for updating the quantizers＇ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-infinity disturbance attenuation level. Both the pre-designed controllers and the quantizers＇ parameters are constructed in a decentralized manner, depending on local information.

Secure control for discrete-time hidden Markov jump systems subject to replay attacks via output feedback

This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loopsystems are stochastically stable with or without replay attacks. Firstly, the tampered sensorsunder replay attacks can be identified via the proposed detection method. Then, an asynchronousstatic output feedback controller is designed, which can eliminate the negative impactcaused by replay attacks in view of the detection results. Based on the linear matrix inequalitytechnique, some sufficient conditions which ensure the closed-loop systems are stochasticallystable and meet a given H∞ performance are established. Finally, a numerical example and apractical example are given to verify the effectiveness and superiority of the proposed method.

Robust H_∞ control for a class of nonlinear singular system with uncertain parameters

The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.

Robust power control method for wireless sensor networks with static output feedback

This paper proposed distributed strategies for the joint control of power and data rates in a wireless sensor network. By adapting a linear state-space model to describe the network dynamics, the power controller with static output feedback is designed in the case that the transmission signal are not always available and the estimation of the unmeasured states constitutes a crucial task in the network. The existence of the power controller is formulated as the feasibility of the convex optimization problem, which can be solved via a linear matrix inequality （LMI） approach. The proposed algorithm also caters to the uncertainties in the network dynamics. Numerical examples are given to illustrate the effectiveness of the proposed methods.

基于线性矩阵不等式的环形永磁力矩电机的H_2/H_∞静态输出反馈控制

针对直接驱动数控转台用环形永磁力矩电机易受负载扰动及自身参数变化影响的特点,文中基于线性矩阵不等式(linear matrix inequality,LMI),设计了一个多目标混合H2/H∞静态输出反馈控制器,该控制器可使闭环系统的极点均落在预先选定的线性矩阵不等式区域D内来实现极点配置。所设计的多目标控制器同时考虑了闭环系统的极点位置和2个重要的鲁棒性能指标(H2和H∞范数),不但保证系统的稳定型和快速性,还使系统对外界及自身扰动具有较强的鲁棒性,在很大程度上解决快速性和鲁棒性之间的矛盾。仿真结果及分析表明,所提出控制器满足高精度直接驱动数控转台用环形永磁力矩电机伺服系统对快速性和鲁棒性的要求。

离散广义分段仿射系统的静态输出反馈控制

为了消除离散广义分段仿射系统的非正则性和非因果性对控制系统性能的不利影响,研究了一类具有参数不确定离散广义分段仿射系统的鲁棒静态输出反馈控制问题.基于分段Lyapunov函数、投影定理和几个基本引理,提出了两种方法来设计使具有参数不确定广义分段仿射系统鲁棒容许的静态输出反馈控制器.利用这两种方法得到的控制器不仅可以保证系统的稳定性,而且可以保证系统的正则性和因果性.通过求解一组包含参变量的LMIs,可以得到保证广义分段放射系统容许的反馈控制器增益.仿真结果证明了所提设计方法的有效性.

基于单步法的车辆主动悬架有限频域静态输出反馈控制

针对车辆主动悬架系统,提出了基于单步法求解的静态输出反馈有限频域H∞控制器设计方法。由于现有的有限频域H∞控制定理含有双线性项,且全状态反馈控制增益并不满足单步法的充分条件,导致静态输出反馈问题无可行解。文中应用GKYP引理给出了一个新的基于静态输出反馈的有限频域H∞控制定理。该定理可采用单步线性矩阵不等式LMI直接求解,相对于传统的迭代LMI及CCL算法,极大地简化了设计过程。借助状态反馈信息,避免了初始求解的不可行性。最后,通过数值算例及台架试验验证了该方法的可行性。

广义系统的时滞依赖静态输出反馈控制

针对一类不确定线性广义时滞系统,给出了静态输出反馈控制器的设计方法.首先基于标称广义时滞系统的稳定条件,以受限线性矩阵不等式形式,给出闭环广义时滞系统正则、无脉冲且渐近稳定的充分条件,同时利用受限矩阵不等式的可行解给出静态输出反馈控制律的一个参数化表示;其次,利用矩阵的正交补,把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式(LMIs)的可行解;最后应用数值实例说明了所给方法的有效性和正确性.

基于ILMI算法的车辆半主动悬架静态输出反馈控制

针对采用磁流变阻尼器的1/4汽车半主动悬架模型进行振动控制分析。利用迭代线性矩阵不等式(ILMI)算法在输出反馈控制中的求解优势,提出基于ILMI算法的半主动悬架静态输出反馈控制方法。仿真结果表明,结合合适的控制算法,采用磁流变阻尼器的半主动悬架系统有效地改善了汽车驾驶平顺性和乘坐舒适性。

建筑结构振动系统的多重叠分散静态输出反馈H_∞控制方法

采用分散控制方案能有效解决大尺度土木结构在地震作用下的结构振动控制问题。本文将静态输出反馈、重叠分散控制方法、线性矩阵不等式方法和H∞范数控制算法相结合,提出了多重叠分散静态输出反馈H∞控制方法。通过对状态矩阵添加一个微小的扰动,解决了在求解相应的线性矩阵不等式(LMI)时所遇到的计算困难问题。文中对20层Benchmark建筑结构模型进行数值模拟与计算。结果表明,部分输出反馈控制、重叠静态输出反馈控制和多重叠静态输出反馈控制均获得了与全状态集中控制相近的控制效果,减少了计算成本和控制器设计的复杂性。

不确定变时滞系统的模糊静态输出反馈保性能可靠控制

针对一类含有执行器故障的变时滞不确定性T-S模糊模型,采用静态输出反馈的并行分布补偿器(PDC)结构,研究了其模糊静态输出反馈保性能可靠控制律的设计问题。通过定义一类时滞相关Lyapunov-Kra-sovskii函数,基于线性矩阵不等式(LMI),给出了模糊静态输出反馈保性能可靠控制器存在的条件,所设计的控制器可保证在正常和执行器故障情况下,闭环系统都能渐近稳定,并且正常保性能上界小于故障保性能上界。仿真实验验证了该设计方法的有效性。

半主动直接输出反馈变结构控制电流变阻尼器减振研究

针对多层结构电流变阻尼器减振系统运动状态难以完全实时测量、扰动存在不确定性、系统参数容易出现摄动以及阻尼器连续可调的特点,提出了半主动直接输出反馈变结构控制策略,根据滑模运动方程稳定的Hurwitz判据选择滑模梯度参数,实现控制与扰动完全解耦;饱和非线性环节使阻尼器阻尼力不超调;阻尼力对主结构做负功控制规则保证主结构最佳减振。仿真分析表明,电流变阻尼器减振控制系统效果明显,不仅对扰动具有自适应性,而且对系统参数摄动也具有很强的鲁棒性。

小型无人直升机的静态H_∞输出反馈控制

针对小型无人直升机系统易受外界干扰影响的问题,用H_∞控制理论的静态输出反馈控制算法来实现其高性能控制。基于线性时不变系统的静态H_∞输出反馈控制理论,给出了直升机在悬停状态下辨识所得的线性模型,并根据此模型对其内外回路进行了控制器设计;对所设计的控制策略进行了仿真,实现了无人直升机的轨迹跟踪控制。结果表明,静态H_∞输出反馈控制策略具有对扰动抑制能力强、控制精度高、鲁棒性好等特点,适用于无人直升机的抗干扰控制。

基于迭代线性矩阵不等式的模糊静态输出反馈控制

对于一类状态矩阵、输入矩阵和扰动输入矩阵中均含有不确定项的离散T-S模糊系统,研究了静态输出反馈控制的二次稳定性问题。以矩阵不等式的形式给出的充分条件保证了基于该模糊系统的静态输出反馈控制器的存在性。该充分条件不但简单,而且考虑到了各个模糊子系统之间的相互作用。最后,使用迭代线性矩阵不等式(ILMI)的方法,通过数值仿真算例证明了该设计方法的正确性及有效性。