Gramian‐based model order reduction of parameterized time‐delay systems

Time‐delay systems (TDSs) frequently arise in circuit simulation especially in high‐frequency applications. Model order reduction (MOR) techniques can be used to facilitate the simulation of TDSs. On the other hand, many kinds of variations, such as temperature and geometric uncertainties, can have significant impact on the transient responses of TDSs. Therefore, it is important to preserve parametric dependence during the MOR procedure. This paper presents a new parameterized MOR scheme for TDSs with parameter variations. We derive parameterized reduced‐order models (ROMs) for TDSs using balanced truncation by approximating the Gramians in the multi‐dimensional space of parameters. The resulting ROMs can preserve the parametric dependence, making it efficient for repeated simulations under different parameter settings. Numerical examples are presented to verify the accuracy and efficiency of our proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Fully parameterized fixed‐order controller design for H∞ loop shaping method using frequency responses—extension to MIMO systems

Robust control is often applied to systems with uncertainties and disturbances. Above all, the H∞ loop shaping method is known to achieve good control performance and robustness. In this method, the final controller consists of weighting functions and a stabilizing controller. The stabilizing controller is derived for the shaped plant to suppress the H∞ norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, and so on. In addition, the stabilizing controller improves robust stability margin while keeping gain characteristic of the shaped plant if weighting functions are suitable. As a result, the closed‐loop system is well‐balanced between good tracking and robustness. However, a final controller tends to be high‐order. For this problem, reduction techniques are often applied to the final controller. In this case, performance and stability is not always adequately evaluated due to errors by the controller reduction. This paper proposes a fully parameterized fixed‐order controller design method using frequency responses of the plant. We formulate a design problem for multi‐input–multi‐output systems as an optimization problem. Therefore, we can directly design a low‐order controller from frequency responses using the iterative LMI optimization. Accordingly, we can avoid to deteriorate the evaluation of performance and stability.     

Guaranteed cost control for large‐scale systems under control gain perturbations

The guaranteed cost control problem of the decentralized robust control for large‐scale systems with the norm‐bounded time‐varying parameter uncertainties and a given quadratic cost function is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that decentralized local state feedback controllers can be obtained by solving the LMI. The problem of guaranteed cost control for large‐scale systems under the gain perturbations is also considered. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 43–57, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10265     

Design of multi‐input multi‐output minimum‐phase state control system with decoupling and feedforward compensation

This paper discusses the design of decoupling control for a multi‐input multi‐output (MIMO) linear system. A new configuration of the prepositional tandem matrix is presented as a decoupling compensator, and minimum‐phase state control is applied to the resulting decoupled system. In general, non‐minimum‐phase characteristics often accompany decoupled systems. Feedforward compensation makes the non‐minimum‐phase effect of each decoupled scalar system change to the delay time. A numerical example is given for the MIMO linear system, which conventionally results in non‐minimum‐phase systems. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 176(2): 53–61, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21117     

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

This article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional‐order competitive type‐neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov‐Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.     

Observer design for neutral‐type neural networks with discrete and distributed time‐varying delays

This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method.     

Transient analysis of multi‐state dc–dc converters using system energy characteristics

The study of multi‐state dc–dc power conversion techniques is restricted by the complicated inner switching behaviors. This paper presents a general and unified transient analysis for various sorts of multi‐state dc–dc converters from a viewpoint of their system energy characteristics. With the applications to the boost converters, the proposed analytical method has indicated its advantages of high convenience and practicability to the multi‐state converters. The generalized concepts of system energy parameters of dc–dc converters are introduced and applied to the transient analysis. Consequently, the expressions of system model parameters of multi‐state dc–dc converters are deduced. The new 2nd order transfer functions are obtained to describe the large‐ and small‐signal mathematical models accurately. The model simulation and experimental results are provided to support the theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

两轮自平衡机器人系统非脆弱控制器设计

以两轮自平衡机器人系统为研究对象,提出了一种基于线性矩阵不等式（linear matrix inequality,LMI）技术的非脆弱控制器设计方法。通过有效的矩阵不等式变换技术,利用Lyapunov函数方法,将基于观测器的控制器存在条件以矩阵不等式的形式给出。不同于已有的控制器设计方法,充分考虑了控制器存在的不确定项扰动,即非脆弱问题。所设计的控制器在存在不确定摄动的情况下,仍能保证系统的稳定性。最后,通过MATLAB软件对本文提出方法的有效性进行仿真验证。     

Passivity–preserving interpolation‐based parameterized model order reduction of PEEC models based on scattered grids

The increasing operating frequencies and decreasing IC feature size call for 3‐D electromagnetic (EM) methods, such as the Partial Element Equivalent Circuit (PEEC) method, as necessary tools for the analysis and design of high‐speed systems. Very large systems of equations are often generated by 3‐D EM methods and model order reduction (MOR) techniques are commonly used to reduce such a high model complexity. A typical design process includes optimization and design space exploration, and hence requires multiple simulations for different design parameter values. Traditional MOR techniques perform model reduction only with respect to frequency and such design activities call for parameterized MOR (PMOR) methods that can reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We present a novel PMOR technique applicable to the PEEC method that provides parametric reduced order models, stable and passive by construction, over a user defined design space. We treat the construction of parametric reduced order models on scattered design space grids. Pertinent numerical examples validate the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

A Green's function‐based method for the transient analysis of plane waves obliquely incident on lossy and dispersive planar layers

This paper presents a new methodology for the transient analysis of plane waves obliquely incident on a planar lossy and dispersive layer. The proposed model is based on the Sturm–Liouville problem associated with the propagation equations. Green's function is calculated in a series form and the open‐end impedance matrix is obtained as the sum of infinite rational functions. This form permits an easy identification of poles and residues. Furthermore, the knowledge of poles leads to the development of a model order reduction technique by selecting only the dominant poles of the system. The pole–residue representation is converted into a state‐space model that can be easily interfaced with ordinary differential equation solvers. The numerical results confirm the effectiveness of the proposed modeling technique. Copyright © 2008 John Wiley & Sons, Ltd.     

A new algorithm for shot noise removal in medical ultrasound images based on alpha‐stable model

Ultrasonic images are generally affected by multiplicative shot noise. Shot noise filtering is thus a critical pre‐processing step in medical ultrasound imagery. This paper analyses and models the coefficients of 2‐D multi‐resolution wavelet decomposition of logarithmically transformed images using alpha‐stable distribution model. Consequently, we propose a new function that performs a non‐linear operation on the data of classifying the coefficients, thus achieving a novel form of noise removal based on multi‐resolution wavelet decomposition and the alpha‐stable model. We compare our new technique with current shot noise reduction methods applied on actual ultrasound medical images and simulations results show that the proposed new method is more robust than the methods based on Gaussian assumption. Copyright © 2006 John Wiley & Sons, Ltd.     

Sensor fault diagnosis and fault‐tolerant control for stochastic distribution time‐delayed control systems

In this paper, a new fault diagnosis and fault‐tolerant control method based on the model equivalent transformation is proposed for the stochastic distribution time‐delayed control system, in which the random delay between the controller and the actuator and the external disturbance is considered. The system is modeled by using a linear B‐spline to approximate the probability density function (PDF) of system output. The original system is transformed into an equivalent system without random delay based on the Laplace transformation method. Then, the equivalent system that is converted to the augmentation system with a new state variable is introduced. The observer is designed to estimate the fault information based on the augmentation system. Observer gain matrices and controller parameters are obtained by solving the linear matrix inequality. The PI control algorithm is used to make the PDF of the system output track the desired distribution. Finally, the validity of the proposed method is verified by computer simulation results.     

Compact model order reduction of weakly nonlinear systems by associated transform

We advance a recently proposed approach, called the associated transform, for computing slim projection matrices serving high‐order Volterra transfer functions in the context of weakly nonlinear model order reduction (NMOR). The innovation is to carry out an association of multivariate (Laplace) variables in high‐order multiple‐input multiple‐output transfer functions to generate univariate single‐s transfer functions. In contrast to conventional projection‐based NMOR which finds projection subspaces about every s_i in multivariate transfer functions, only that about a single s is required in the proposed approach. This leads to much more compact reduced‐order models without compromising accuracy. Specifically, the proposed NMOR procedure first converts the original set of Volterra transfer functions into a new set of linear transfer functions, which then allows direct utilization of linear MOR techniques for modeling weakly nonlinear systems with either single‐tone or multi‐tone inputs. An adaptive algorithm is also given to govern the selection of appropriate basis orders in different Volterra transfer functions. Numerical examples then verify the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Order reduction of the dynamic model of a linear weakly periodic system-part I: general methodology

A methodology is presented for the order reduction of the dynamic model of a linear weakly periodic system obtained by linearization about the nonsinusoidal periodic steady state. It consists of two stages. First, the time-invariant part of the original full-order system is approximated by a reduced system by using singular value decomposition techniques. Then the time-varying part of the reduced system is calculated by using a Gauss-Seidel technique. The issues of sparsity, convergence, and accuracy are analyzed. The example used for illustration serves to demonstrate the efficiency of the new method.     

T-S模糊模型控制器的LMI设计方法

为了探讨模糊控制系统的稳定性分析和设计方法,依据模糊控制理论,把离散T-S模糊模型看成是一个线性不确定系统,提出了基于线性矩阵不等式和分段Lyapunov函数的模糊控制器设计方法.将闭环控制系统的稳定要求、性能指标约束条件统一到线性矩阵不等式的框架内,通过求解线性矩阵不等式族获得控制器参数.该方法能够保证系统全局稳定,并且具有良好的动态和稳态性能.     

Robust exponential stability for discrete‐time interval BAM neural networks with delays and Markovian jump parameters

This paper investigates the problem of global robust exponential stability for discrete‐time interval BAM neural networks with mode‐dependent time delays and Markovian jump parameters, by utilizing the Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) approach. A new Markov process as discrete‐time, discrete‐state Markov process is considered. An exponential stability performance analysis result is first established for error systems without ignoring any terms in the derivative of Lyapunov functional by considering the relationship between the time‐varying delay and its upper bound. The delay factor depends on the mode of operation. Three numerical examples are given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

A hybrid adaptive sampling algorithm for obtaining reduced order models for systems with frequency dependent state‐space matrices

This paper proposes a hybrid adaptive sampling algorithm to automate the generation of reduced order models for systems described by large‐scale frequency dependent state‐space models. The evaluation of the frequency dependent state‐space model for each frequency sample can be computationally expensive. The distribution of frequency samples must be optimized to avoid oversampling and undersampling. In order to have an optimum number of frequency samples, the proposed algorithm uses the reflective exploration technique for the adaptive selection of samples, and the sampling is further refined using a binary search to validate the frequency dependent reduced order models. Projection‐based model order reduction techniques are used for obtaining the reduced order model. The projection matrix for each frequency sample is merged to obtain a common projection matrix for all samples. However, in certain cases when the number of sample points increases, the merged projection matrix also increases in dimension and might fail to provide a satisfactory reduction in model size. Thus, the merged projection matrix is truncated based on its singular values to obtain a compact common projection matrix. Then, the reduced order state‐space matrices per frequency are interpolated over the frequency range of interest to obtain the system response. Pertinent examples validate the proposed hybrid adaptive sampling algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

基于LMI的多目标模糊状态反馈控制器设计研究

为实现使系统同时满足多目标控制要求,并避免设计过程多次反复的目的,提出了基于LMI的多目标模糊状态反馈控制器的设计方法。该方法在TS模糊模型的基础上,将闭环控制系统的稳定性、抗干扰性及极点配置的要求统一到一个线性矩阵不等式组中,通过求解线性矩阵不等式组获得满足要求的控制器参数,利用PDC方法得到整个系统的非线性模糊状态反馈控制器。应用于磁悬浮轴承系统,通过仿真试验,验证了该方法的有效性,系统同时满足稳定性、抗干扰特性及过渡过程特性多个目标要求。