具有滞后型执行机构的Lurie控制系统的鲁棒绝对稳定性

本文对于具有滞后型执行机构的不确定性Lurie控制系统，构造了一个关于Lyapunov泛函中自由参数的LMI。通过这个LMI的解来构造Lyapunov泛函保证系统的鲁棒绝对稳定性。在此基础上，获得了保证系统绝对稳定的鲁棒扰动界的LMI，并给出了利用迭代法获得鲁棒扰动界的方法。最后给出一个实例说明本文方法的有效性。     

线性时滞系统的耗散控制

从全新的二次型供给率的耗散角度，研究了线性时滞系统的二次稳定性和耗散控制问题，给出了线性矩阵不等式(LMI)形式的充分条件。而且，考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题，同样给出了LMI形式的充分条件，并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。     

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.     

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。     

Synchronization analysis of coupled connected neural networks with mixed time delays

In this paper, the global exponential synchronization of coupled connected neural networks with both discrete and distributed delays is investigated under mild condition, assuming neither the differentiability and strict monotonicity for the activation functions nor the diagonal for the inner coupling matrices. By employing a new Lyapunov–Krasovskii functional, applying the theory of Kronecker product of matrices and the linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions in LMI form are obtained for global exponential synchronization of such systems. Moreover, the decay rate is estimated. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using efficient Matlab LMI toolbox, and no tuning of parameters is required. In addition, the proposed results generalize and improve the earlier publications. An example with simulation is given to show the effectiveness of the obtained results.     

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.     

Convex Design of a Robust Antiwindup Controller for an LFT Model

In the context of a closed-loop LFT model, an LMI technique is proposed for the synthesis of a static or dynamic antiwindup controller, which can be seen as a nontrivial extension of existing LMI methods for designing a robust filter or feedforward controller. A missile example is given to illustrate the feasibility of the technique.     

具有Neumann边界的分布参数切换系统反馈镇定

通过构造Lyapunov函数,利用线性矩阵不等式,对一类具有Neumann边界的分布参数切换系统给出了状态反馈镇定的充分条件。该条件用一组线性矩阵不等式表示,将分布参数切换系统状态反馈镇定问题转化为一组线性矩阵不等式的可行解问题,可借助Matlab中线性矩阵不等式工具箱求解,因而容易检验和应用。最后通过数值算例,验证所提出设计方法的有效性。     

Lagrange stabilisation for uncertain phase-controlled systems

In this article, we are concerned with the Lagrange stabilisation problem for phase-controlled systems with parameter uncertainties. By using the Kalman–Yakubovich–Popov lemma, the frequency-domain conditions for Lagrange stability of nominal phase-controlled systems are converted into linear matrix inequality (LMI) conditions. The allowable parameter uncertainty bounds for controllability and observability, as well as LMI conditions for Lagrange stability of uncertain phase-controlled systems, are presented. A controller design strategy based on the LMI method is proposed such that the uncertain phase-controlled systems are Lagrange stabilised. A numerical example is provided to demonstrate the effectiveness of the proposed results.     

A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence

In previous works we have proposed a robust stability condition for linear time-invariant discrete-time systems which makes use of a Lyapunov function with linear dependence on the uncertain parameters. This condition is expressed as a set of linear matrix inequalities (LMI) where an additional variable is kept common to all LMI. These features have enabled the development of successful robust filtering and control algorithms. In this short note we investigate possible extensions of this stability condition to handle Lyapunov functions with arbitrary parameter dependence while keeping a variable common to all LMI. By showing that feasibility of the original condition is indeed necessary for the existence of a family of robust stability conditions where the Lyapunov function can have arbitrary dependence on the uncertain parameters, we conclude that no such extensions are possible.     

采用LMI的鲁棒预测控制综合方法

本文简单叙述了线性矩阵不等式（LMI）在控制理论中应用的历史,重点介绍了LMI的原理及其在鲁棒预测控制综合方法中应用的一种新方法,举例说明了如何在预测控制综合方法中应用LMI。本文可作为在鲁棒预测控制中应用LMI和用微机实现鲁棒预测控制算法的参考。     

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。     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

Sufficient LMI conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems

In this note, sufficient conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H/sub /spl infin// output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H/sub /spl infin// output feedback control and simultaneous H/sub /spl infin// output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.     

Global exponential stability for neutral-type BAM neural networks with time-varying delays

In this article, the global exponential stability of neutral-type bidirectional associative memory (BAM) neural networks with time-varying delays is analysed by utilizing the Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach. New sufficient conditions ensuring the global exponential stability of neutral-type BAM neural networks is obtained by using the powerful MATLAB LMI control toolbox. In addition, an example is provided to illustrate the applicability of the result.     

General quadratic performance analysis and synthesis of differential algebraic equation (DAE) systems

In this paper, control of linear differential-algebraic-equation systems, subject to general quadratic constraints, is considered. This setup, especially, includes the H_∞ control problem and the design for strict passivity. Based on linear matrix inequality (LMI) analysis conditions, LMI synthesis conditions for the existence of linear output feedback controllers are derived by means of a linearizing change of variables. This approach is constructive: a procedure for the determination of controller parameterizations is given on the basis of the solution of the LMI synthesis conditions. A discussion of the possible applications of the presented results concludes the paper.     

Stability Conditions for LMI-Based Fuzzy Control From Viewpoint of Membership Functions

In this paper, we investigate the stability conditions for linear matrix inequality (LMI)-based fuzzy control design. Especially, we focus on the dependence of the stability upon membership functions. In general, the membership functions in the rule bases of Takagi-Sugeno (T-S) fuzzy model and controllers are the same and restricted between 0 and 1. In contrast to this setting, we obtain some new results when different membership functions are considered and their values lying outside the interval of [0,1] are allowed. Applying Lyapunov equation and a convex hull of fuzzy subsystems, we first establish a relationship between the stable interval characteristic polynomial and a set of feasible LMIs. Then Kharitonov's theorem gives an insight for the solvability of stabilization problems using LMI-based design and, this leads that the membership functions have an influence on stability. On the other hand, the LMI condition leads to the well-known results for LMI-based fuzzy control design. We further indicate that the different LMI conditions arise due to the same or different membership functions and find their own applications on adaptive fuzzy control. Finally, if the unit interval constraint is removed, an LMI condition for global stability is obtained     

Robust observer-based control of systems with state perturbations via LMI approach

In this note, the observer-based control for a class of uncertain, linear systems is considered. Exponential stabilizability for the systems is studied and the convergence rate of the system is estimated. A linear matrix inequality (LMI) approach is used to design the observer-based control. The control and observer gains are given from LMI feasible solution. A numerical example is given to illustrate our results.     

Pseudo-state feedback stabilization of commensurate fractional order systems

This paper addresses the problem of pseudo-state feedback stabilization of commensurate fractional order systems (FOS). In the proposed approach, Linear Matrix Inequalities (LMI) formalism is used to check if the pseudo-state matrix eigenvalues belong to the FOS stability region of the complex plane. A review of LMI stability conditions is first proposed for fractional order 0<ν<1 and 1<ν<2. The paper then focuses particularly on the case 0<ν<1 as the stability region is non-convex and associated LMI condition is not as straightforward to obtain as in the case 1<ν<2. A new LMI stability condition is thus proposed. Based on this condition, a necessary and sufficient LMI method for the design of stabilizing controllers is given. This method paves the way for extension to FOS of various LMI-based results. Among these possible extensions, a first result on robust control of polytopic fractional order systems is given in this paper.     

Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities

A randomized approach is considered for a feasibility problem on a parameter-dependent linear matrix inequality (LMI). In particular, a gradient-based and an ellipsoid-based randomized algorithms are improved by introduction of a stopping rule. The improved algorithms stop after a bounded number of iterations and this bound is of polynomial order in the problem size. When the algorithms stop, either of the following two events occurs: (i) they find with high confidence a probabilistic solution, which satisfies the given LMI for most of the parameter values; (ii) they detect in an approximate sense the non-existence of a deterministic solution, which satisfies the given LMI for all the parameter values. These results are important because the original randomized algorithms have issues to be settled on detection of convergence, on the speed of convergence, and on the assumption of feasibility. The improved algorithms can be adapted for an optimization problem constrained by a parameter-dependent LMI. A numerical example shows the efficacy of the proposed algorithms.