Static realization of dynamic precompensators

The problem of static realization of dynamic precompensators on a controllable pair (A,B) is considered. Necessary and sufficient conditions for the solution of this problem in the general case are given. These conditions are constructive, and they apply not only to invertible precompensators but also to those which are only left invertible     

Feedback realization of nonsingular precompensators for linearsystems with delays

The problem of realization of dynamic precompensators for linear systems with delays by static or dynamic state feedback, and static output feedback, is considered. Necessary and sufficient conditions for the solutions are given     

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.     

双线性系统的静态分散输出控制

研究了一类T-S双线关联系统的静态输出控制反馈问题。应用分散控制理论,得到了闭环关联大系统Lyapunov稳定的充分条件。相应的分散模糊控制器可由线性矩阵不等式(LMD的解得到。最后,由数例仿真验证了所提方法的有效性。     

L1 synthesis of a static output controller for positive systems by LMI iteration

An approach to find a static output feedback gain that makes the feedback system positive and minimizes the L₁ gain is proposed. The problem of finding a static output feedback gain has 3 aspects: stabilizing the system, making the system positive, and then minimizing the L₁ gain. Each subproblem is described by bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix or vector. Linear matrix inequality (LMI) that is sufficient to satisfy bilinear matrix inequality is derived using a convex‐concave decomposition, and the feedback gain sequence is calculated by an iterative solution of LMI. The sequence of the upper bounds on the design parameter is guaranteed to be monotonically nonincreasing for each algorithm. Similarly, 2 other LMIs are derived for each subproblem using another convex‐concave decomposition and PK iteration. The effectiveness of these algorithms is illustrated via several numerical examples.     

线性系统静态输出反馈镇定的LMI方法

利用无约束条件的线性矩阵不等式（LMI）研究了W－问题和P－问题,而后者的解可用来设计静态输出反馈（SOF）镇定控制,作为一个应用考虑了不确定系统的静态输出反馈问题,给出了依赖于LMI条件的SOF设计方法。     

A new perspective on static and low order anti-windup synthesis

By viewing the anti-windup problem as a decoupled set of subsystems and relating this configuration to a general static anti-windup set-up, LMI conditions are established which guarantee stability and performance of the resulting closed-loop system. The approach taken, and the mapping used for the performance index, are logical and intuitive–-and, it is argued, central to the ‘true’ anti-windup objective. The approach enables one to construct static anti-windup compensators in a systematic and numerically tractable manner. The idea is extended to allow low-order anti-windup compensators to be synthesized, which, while being sub-optimal, can improve transient performance and possess several desired properties (such as low computational overhead and sensible closed-loop pole locations). In addition, low-order anti-windup synthesis is often feasible when the corresponding static synthesis is not.     

基于输出反馈的直升机变结构控制律设计

针对直升机的小扰动模型,设计了静态输出反馈滑模控制器（SOFSMC）。利用参考模型,实现了直升机的相关动态指标。针对滑模面的设计问题,将其等价地转化为一组双线性矩阵不等式（BLMI）,并采用迭代线性矩阵不等式（ILMI）技术来求解。针对控制律的综合问题,给出了一种基于单位向量法的控制律,并通过引入线性反馈来保证系统进入滑动模态后线性控制部分与标称系统的线性控制部分的一致性。仿真结果验证了该方法的有效性。     

超混沌系统的一种模糊滑模控制

采用T-S模糊模型对超混沌系统建模,用区域极点配置技术和线性矩阵不等式技术构造满足动静态性能要求的滑模面．在此基础上设计满足指数趋近律的模糊滑模控制器．通过将该控制器应用到Rossler超混沌系统中,验证了所提出方案的有效性.     

H2/H∞保性能控制理论在静止无功发生器控制中的应用

利用H₂/H_∞保性能控制理论和直接反馈线性化, 给出了单机无穷大系统中, 具有参数摄动的静止无功发生器(STATCOM)的非线性控制模型. 使用MATLAB软件得出H₂/H_∞保性能控制律, 表示为线性矩阵不等式(LMI).在扰动及参数摄动的条件下进行了仿真. 结果表明这种控制方法同时具有鲁棒性和最优性能, 降低了单纯H_∞控制方法的保守性, 提高了电力系统的稳定性, 并满足电压精度的要求.     

Output feedback stabilization for discrete singular systems with random abrupt changes

The problem of static output feedback control is investigated for discrete singular systems with Markovian jump. Two necessary and sufficient conditions for the discrete singular Markovian jump system to be regular, causal and stochastically stable are proposed in terms of linear matrix inequality (LMI) approach. Two kinds of design methods of the desired mode‐independent static output feedback controller are given. The explicit expressions for the desired controller are also given. Numerical examples are proposed to show the validness of the developed results. Copyright © 2009 John Wiley & Sons, Ltd.     

基于结构L yapunov 矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题，这导致了一个非线性最优化问题，是无法直接求解的．针对线性时不变系统(LTI)，深入研究这两个矩阵不等式的关系，通过构造一个结构Lyapunov矩阵，给出了一个问题有解的充分条件，并在此基础上提出一个静态输出反馈镇定算法．利用线性矩阵不等式(LMI)方法，可直接求解出相应的输出反馈增益．数值实例证明了该方法的有效性．     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

Convergent relaxations of polynomial matrix inequalities and static output feedback

Using a moment interpretation of recent results on sum-of-squares decompositions of nonnegative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve nonconvex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to the global optimum. Results from the theory of moments are used to detect whether the global optimum is reached at a given LMI relaxation, and if so, to extract global minimizers that satisfy the PMI. The approach is successfully applied to PMIs arising from static output feedback design problems.     

Optimization of static output feedback using substitutive LMI formulation

This note proposes a new design tool for optimizing static output feedback using a linear matrix inequality (LMI) formula called substitutive LMI. A matrix inequality derived from static output feedback is not usually linear. Adding a positive definite term including auxiliary variables, the matrix inequality is transformed into an LMI with respect to the positive definite matrix and the static output feedback gain. An iterative calculation algorithm is given to solve the substitutive LMI. In this note, designs of the static output feedback gain are shown in the frame of H/sub /spl infin// and H/sub 2/ syntheses. A numerical example is shown to demonstrate the effectiveness of the proposed technique.     

基于线性矩阵不等式的分散H2/H∞控制的次优设计

用线性矩阵不等式(LMI)方法研究大系统分散H2/H∞控制问题,提出了存在分散 H2/H∞状态反馈控制器的参数化定理和两种基于LMI的设计方法:直接LMI方法和迭代LMI (ILMI)方法.所获得的控制器具有块对角结构,闭环系统稳定且能优化闭环系统的H2/H∞性 能指标,示例说明了该算法的应用.     

基于区域极点约束的鲁棒H2控制

考虑了在区域极点约束下状态反馈的鲁棒H2控制问题.分别对含多面体不确定性的连 续和离散系统进行了讨论.基于LMI,给出了存在参数相关的Lyapunov矩阵的充分条件.利用 LMI凸优化方法的解,所得静态反馈控制器,不仅保证闭环系统的极点在-给定区域内,而且还 使性能指标H2的一上界达到最小.     

具有次优保性能滑动模态的静态输出反馈滑模控制

针对一类不确定系统,提出了一种具有次优保性能滑模面的静态输出反馈滑模控制方法.首先将滑模面的设计问题等价为一个对称矩阵的求解问题,基于等效控制法,推导了保性能滑模面存在的充分条件.然后基于迭代线性矩阵不等式(iterative linear matrix inequality,ILMI)方法,给出了次优保性能线性滑模面的求解算法,最后基于线性矩阵不等式(linearmatrix inequality,LMI)方法,设计了输出反馈滑模控制器,使得闭环系统渐近稳定且切换函数能在有限时间内到达零.该方法首次实现了输出反馈滑模面的优化,且具有保守性小、无需对被控系统模型进行坐标变换的优点.仿真结果验证了本文方法的优越性.     

Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach

This paper addresses the problem of designing robust static output-feedback controllers for nonlinear discrete-time interval systems with time delays both in states and in control input. In the approach, we do not directly employ the Lyapunov approach, as do in most of traditional fuzzy control design approaches. Instead, sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed-loop fuzzy system. The stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the Matlab linear matrix inequality (LMI) toolbox. Finally, an example is provided to illustrate the effectiveness of the proposed approach.     

Output feedback decentralized stabilization: ILMI approach

In this paper, the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach. A necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time-invariant large-scale systems. It is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality. The extension of the result to control is studied. An iterative LMI algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain. Examples show the effectiveness of the algorithm.