离散时滞系统的无记忆稳定化控制器设计

对离散时滞系统,研究无记忆状反馈稳定化控制律的设计问题,导出了控制律存在的条件,并证明了该条件等价于一个线性矩阵不等式系统的可解性问题。通过这个线性矩阵不等式系统的可行解,给出了稳定化控制律的构造方法,进而,通过建立和求解一个凸优化问题,提出了具有较小反馈增益参数的无记忆状态反馈控制律的设计方法。     

不确定系统具有圆盘区域极点约束的鲁棒控制

对一类不确定线性系统,提出了存在状态反馈控制律,使得闭环系统的所有极点均位 于一给定圆盘中的一个充分必要条件.结合控制律反馈增益参数极小化的要求,建立了一个具 有线性矩阵不等式约束的凸优化问题,通过该问题的解,可以构造一个具有较小反馈增益参数 和给定要求的控制律.所提出的方法既可应用到连续系统,也可应用到离散系统.     

不确定时延输出反馈网络化系统保性能控制

研究了一类具有不确定时延的动态输出反馈网络控制系统的保性能控制问题．针对小于等于一个采样周期的不确定时延,利用Lyapunov理论和线性矩阵不等式方法,推导出了动态输出反馈网络控制系统保性能控制律存在的条件,给出了动态输出反馈保性能控制律设计方法．利用LMI工具箱中的目标函数最小化工具,可以求得该类系统优化的保性能控制律参数和优化的性能指标,从而获得该系统的保性能控制律．给出的仿真算例说明了设计方法是有效的所得结果是可行的．     

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.     

不确定离散时间系统的H_2/H_∞最优保性能控制

针对具有两个不同被调输出的一类不确定离散时间系统 ,研究其 H2 / H∞ 状态反馈保性能控制问题。基于线性矩阵不等式处理方法 ,推导出存在 H2 / H∞ 保性能控制律的充分必要条件 ,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的参数化表示。进而通过建立和求解一个凸优化问题 ,给出了 H2 / H∞ 最优保性能控制律设计方法。最后通过一个例子说明了所提出方法的有效性     

不确定离散时滞系统的保性能控制

针对一类具有范数有界不确定性和状态滞后的离散时间线性系统,结合一个二次型 性能指标,采用线性矩阵不等式方法,提出了无记忆状态反馈保性能控制律的存在条件,并利 用一个线性矩阵不等式的解给出了保性能控制律的一个参数化表示.     

不确定离散时间系统的H2/ H∞最优保性能控制

针对具有两个不同被调输出的一类不确定离散时间系统,研究其H2/H∞状态反馈保性能控制问题,基于线性矩阵不等式处理方法。推导出存在H2/H∞保性能控制律的充分必要条件,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的参数化表示,进而通过建立和求解一个凸优化问题,给出了H2/H∞最优保性能控制律设计方法,最后通过一个例子说明了所提出方法的有效性。     

不确定离散时滞系统的状态时滞反馈保性能控制器的设计

对一类同时具有状态时滞和输入时滞的不确定离散时滞系统,提出保性能状态时滞反馈控制律的设计问题。结合一个二次型性能指标,基于Lyapunov函数和线性矩阵不等式处理方法,推出状态时滞反馈保性能控制律存在的条件,并用线性矩阵不等式的可行解给出保性能控制律的构造方法。最后给出一个仿真例子证明该方法的有效性。     

不确定时滞系统的非线性保性能控制

针对一类非线性系统和给定的性能指标,研究其保性能控制问题。基于Lyapunov稳定性理论,采用线性矩阵不等式工具,给出非线性状态反馈保性能控制器存在的一个充分条件,并依据其可行解给出相应保性能控制律的设计方法。建立一个具有线性矩阵不等式约束的凸优化问题,得到非线性系统的最优保性能控制律。仿真示例表明该方法的可行性。     

不确定离散时间系统的H_2/H_∞最优保性能控制

针对具有两个不同被调输出的一类不确定离散时间系统 ,研究了其 H2 /H∞ 状态反馈保性能控制问题。基于线性矩阵不等式处理方法 ,导出了存在 H2 /H∞ 保性能控制律的充分必要条件 ,并用一个线性矩阵不等式的可行解给出了所有保性能控制律的一个参数化表示。进而 ,通过建立和求解一个凸化问题 ,给出了 H2 /H∞最优保性能控制设计方法。最后 ,通过一个例子说明了本文所提出方法的有效性     

一类关联时滞组合系统的H_∞滤波

针对当输入噪声为有限能量信号时的渐近稳定的线性滤波器的设计问题,基于Lyapunov稳定性理论,结合线性矩阵不等式技术,提出了一类关联时滞组合系统的H_∞滤波器的设计方案,并利用有界实引理给出了滤波器存在的一个充分条件。为了使得滤波器具有良好的稳态性能,考虑了LMI的优化问题。并将滤波器的设计问题转化为具有线性矩阵不等式约束的凸优化求解问题。通过求解一组LMI,可以得到最优滤波器。     

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．     

An anti-windup technique for LMI regions

The anti-windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities, such as saturation, for a given linear time-invariant plant and controller. This paper presents a linear matrix inequality (LMI) based method that attempts to minimize performance deterioration while explicitly restricting the anti-windup closed loop dynamics. The restriction placed on the dynamics is described via LMI regions, which is a form of regional pole placement. Finally, the techniques discussed in this paper are demonstrated on an electro-hydraulic testbed.     

Reduction of H∞ state feedback control problems for the MIMO servo systems

We deal with H_∞ state feedback control problem for the multi‐input‐multi‐output (MIMO) servo system and discuss the advantages of the facial reduction (FR) to the resulting linear matrix inequality (LMI) problems. In fact, as far as our usual setting, the dual of the LMI problem is not strictly feasible because the generalized plant has always stable invariant zeros. Thus FR is available to such LMI problems, and we can reduce and simplify the original LMI problem to a smaller‐size LMI problem. As a result, we observe that the numerical performance of the SDP solvers is improved. Also, as a by‐product, we obtain the best performance index of the reduced LMI problem with a closed‐form expression. This helps the H_∞ performance limitation analysis. Another contribution is to reveal that the resulting LMI problem obtained from H_∞ control problem has a finite optimal value, but no optimal solutions under an additional assumption. This is also confirmed in the numerical experiment of this paper. FR also plays an essential role in this analysis.     

Low-order robust power system stabilizer for single-machine systems: An LMI approach

This paper describes a linear matrix inequality (LMI) approach to the design of robust loworder power system stabilizers (PSSs), which are used to damp out local-mode oscillations of synchronous generators. The performance of a PSS is expressed as the location of the closed-loop poles, and a single fixed-gain pole-placement controller is synthesized for a wide range of operating conditions. The synthesis results in simultaneous regional pole-placement stabilization through static output feedback, and is formulated as a novel LMI feasibility problem with a rank condition. A penalty method is applied to solve the rank-constrained LMI problem. Numerical experiments with a single machine connected to an infinite bus system were performed to demonstrate the proposed LMI method, and the results were compared with those of previous work.     

Design of high performance linear feedback laws for operation that extends into the nonlinear region of AMB systems

Existing active magnetic bearings (AMBs) operate in the linear region of the magnetic material flux density, which limits the utilization of the bearing capacity. In order to increase the utilization of the bearing capacity and enhance the performance of the AMB system, this paper develops a method for designing high performance linear feedback laws. The resulting feedback laws allow the AMB to operate in its nonlinear region and hence improve the closed-loop performance. We first establish an approximate nonlinear AMB current force response model, and place this nonlinear curve inside a sector formed by two piecewise linear lines. Based on the linear line segments in these two piecewise linear lines, we determine the maximum disturbance that can be tolerated by solving an optimization problem with linear matrix inequality (LMI) constraints. For a given level of disturbance under the maximum tolerable disturbance, we formulate and solve the problem of designing the linear feedback that achieves the highest level of disturbance rejection as another LMI problem. Both $L_2$ disturbances and $L_\infty$ disturbances are considered. Finally, we illustrate our design by both simulation and experimental results.     

一类随机混杂系统的鲁棒方差控制

对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性.     

具有椭圆盘极点约束的线性系统滤波器设计

针对一类线性系统,研究其闭环系统极点具有椭圆盘约束的情况下滤波器设计问题。在极点约束的前提下,控制目标要求闭环系统渐近稳定,并且干扰抑制性能指标小于给定的上界。首先利用有界实引理给出椭圆盘极点约束前提下滤波器的存在条件;其次,利用线性矩阵不等式技术,将滤波器的存在性问题转化成一组线性矩阵不等式(LMI)的可行性问题,根据LMI的可行解,给出滤波器的设计方法,由该方法得到的滤波器满足给定的性能要求;最后,数值算例说明该方法的有效性和可行性。     

H ∞ switching filter design for LPV systems in finite frequency domain

This article studies the problem of finite frequency H _∞ filter design for switching linear parameter varying (LPV) systems with disturbance frequency affected by system parameters. A set of switching filters are designed, each suitable for a specific parameter subregion and a specific finite frequency performance index. A hysteresis switching logic is adopted, and the design problem is finally formulated into linear matrix inequality (LMI) which can be solved efficiently with LMI Control Toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.     

Simultaneous linear-quadratic optimal control design via static output feedback

In this paper, the problem of designing a fixed static output feedback control law which minimizes an upper bound on linear quadratic (LQ) performance measures for r distinct MIMO plants is addressed using linear matrix inequality (LMI) technique. An iterative LMI algorithm is proposed to obtain the solution. Examples are used to demonstrate its effectiveness. Copyright ©1999 John Wiley & Sons, Ltd.