奇异系统的一个实现方法

对于线性时不变奇异系统,给出传递矩阵构造它的最小有限维实现。所提算法的关键是将传递矩阵变成正常的,因而可以享用对正常系统已有实现结果的一些长处。     

Approximate realization based upon an alternative to the Hankel matrix: the Page matrix

The Ho-Kalman algorithm creates a minimum realization of a system, when given a series of deterministic Markov parameters. However, when such a ‘truncated’ series of Markov parameters has been disturbed with noise, an approximating Hankel matrix has to be constructed for applying the realization algorithm. This approximating Hankel matrix has either the improper rank, or it lacks the Hankel structure.Furthermore the Markov parameters are not processed with a constant weighting factor, which implies that the noise filtering is inadequate. In this paper we propose to use an alternative matrix: the Page matrix. It is shown that this method is better suited for handling the noisy Markov parameters. This holds with respect to three aspects: order testing, noise filtering and realization.Even in the deterministic case, the Page matrix offers the advantage of a considerable reduction in computation.     

Singular ℋ︁2 control of discrete‐time systems: From frequency to time domain

Necessary and sufficient conditions for the existence of a minimizing discrete‐time ??₂ control, when assumptions are the internal stabilizability and left‐ and right‐invertibility of transfer matrices G ₁₂ and G ₂₁, are presented. Unlike the existing approach with a transformation into a disturbance decoupling problem with a measurement feedback and internal stability, we use a direct approach: from frequency to time domain. The first main result gives a necessary and sufficient existence condition for ??₂ control: that a minimal realization of the infimal controller is stabilizing. The second main result presents a realization of an optimal controller that has a state observer form, identical to the form of the regular case, except that the state‐feedback gain matrix and the observer gain matrix are replaced by some stabilizing matrices. Copyright © 2009 John Wiley & Sons, Ltd.     

求多输入多输出有理传递函数的最小实现的一种算法

本文叙述了多输入多输出有理传递两数到状态方程的最小实现的方法,在所述的算法中用SVD分解求得最小实现的维数,再求解一系列相当于系数矩阵为上三角阵的线性方程组,得出最小实现的状态方程系数矩阵A、B、C。     

Minimal realizations of transfer-function matrices by means of matrix continued fraction

The matrix continued fraction technique is utilized to obtain the minimal realization of a transfer-function matrix with various inputs and outputs. If the ratio of the rank and the order of a square transfer-function matrix is an integer and there are no numerically ill-conditional elements in the matrix, then the matrix Routh algorithm is applied for the minimal realization. A method is also presented to deal with ill-conditional cases.     

HANKEL矩阵的奇异值分析和系统结构及实现的数值算法

本文通过奇异分解分析了系统结构的定量性质和在数字计算机上计算结构参数及实现时所遇到的数值问题,并指出了结构定量性质和数值稳定性间的关系。本文给出了由HANKEL矩阵奇异值分解所得的几个典型最小实现,提出了一个借助奇异值分解由HANKEL矩阵直接计算结构参数的可靠的数值算法。     

Realization of bilinear stochastic systems

This note considers the problem of realization of bilinear stochastic systems (BLSR). First an explicit statement for the BLSR problem is presented. Next a realization algorithm is developed. In this algorithm the state vector is picked as a basis in the subspace obtained by projecting an appropriately defined past vector onto an appropriately defined future vector. Also, the realization algorithm involves solving a matrix nonlinear equation which is akin to the algebraic Riccati equation, except for one additional term.     

A sufficient condition for the stability of matrix polynomials

A sufficient condition is presented for the stability of the matrix polynomials based on algebraic properties of the matrix coefficients. The stability condition is derived from the Lyapunov theory by a multivariable feedback system that is associated to the matrix polynomial. Illustrative examples are given. A block-Schwarz form related to the matrix polynomial is obtained directly from the given realization algorithm     

Estimating the fundamental matrix based on least absolute deviation

The epipolar geometry is the intrinsic projective geometry between two views, and the algebraic representation of it is the fundamental matrix. Estimating the fundamental matrix requires solving an over-determined equation. Many classical approaches assume that the error values of the over-determined equation obey a Gaussian distribution. However, the performances of these approaches may decrease significantly when the noise is large and heterogeneous. This paper proposes a novel technique for estimating the fundamental matrix based on least absolute deviation (LAD), which is also known as the L₁ method. Then a linear iterative algorithm is presented. The experimental results on some indoor and outdoor scenes show that the proposed algorithm yields the accurate and robust estimates of the fundamental matrix when the noise is non-Gaussian.     

A stochastic realization algorithm via block LQ decomposition in Hilbert space

A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a “block LQ decomposition”. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.     

Comments on ‘New algorithm for minimal balanced realization of transfer function matrix’

Gonzalez and Munro (1990) presented a new algorithm for the minimal balanced realization of a transfer function matrix. We point out that their algorithm fails generically. We also give an alternative algorithm which is both more general and computationally efficient.     

基于三维网格的最短路径并行算法研究

针对三角网格模型,描述了一种求解最短路径问题的并行算法.该算法使用两矩阵相乘思想,利用对邻接矩阵的划分实现算法的并行化,给出了输出路径值和打印路径的过程分析.最后给出了该算法在机群环境下的实现,并联系实际例图,进行了算法性能分析,验证了其具有很好的并行效率.     

H∞ control for linear systems with state saturation nonlinearities

The problem of H_∞ control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H_∞ control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On the matrix feedback shift register synthesis for matrix sequences矩阵序列的矩阵反馈移位寄存器综合问题

In this paper, a generalization of the linear feedback shift register synthesis problem is presented for synthesizing minimum-length matrix feedback shift registers (MFSRs for short) to generate prescribed matrix sequences and so a new complexity measure, that is, matrix complexity, is introduced. This problem is closely related to the minimal partial realization in linear systems and so can be solved through any minimal partial realization algorithm. All minimum-length MFSRs capable of generating a given matrix sequence with finite length are characterized and a necessary and sufficient condition for the uniqueness issue is obtained. Furthermore, the asymptotic behavior of the matrix complexity profile of random vector sequences is determined.     

Reduced-order controllers for the H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H_∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H_∞ control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H_∞ control problems.     

A novel extended precise integration method based on Fourier series expansion for the H2-norm of linear time-varying periodic systems

A new reliable algorithm for computing the H₂-norm of linear time-varying periodic (LTP) systems via the periodic Lyapunov differential equation (PLDE) is proposed. By taking full advantage of the periodicity, the transition matrix of the underlying LTP system associated with the PLDE is effectively computed by developing a novel extended precise integration method based on Fourier series expansion, where the time-consuming work for the computation of the matrix exponential and its related integrals in every sub-interval is avoided. Then, a highly accurate and efficient algorithm for the PLDE is derived using the block form of the transition matrix. Thus, the H₂-norm is evaluated by solving a simple first-order ordinary differential equation. Finally, two numerical examples are presented and compared with other algorithms to verify the numerical accuracy and efficiency of the proposed algorithm.     

Truncated balanced realization of a stable non-minimal state-space system

In this paper we present a numerically reliable algorithm to compute the balanced realization of a stable state-space system that may be arbitrarily close to being unobservable and/or uncontrollable. The resulting realization, which is known to be a good approximation of the original system, must be minimal and therefore may contain a reduced number of states. Depending on the choice of partitioning of the Hankel singular values, this algorithm can be used either as a form of minimal realization or of model reduction. This illustrates that in finite precision arithmetic these two procedures are closely related. In addition to real matrix multiplication, the algorithm only requires the solution of two Lyapunov equations and one singular value decomposition of an upper-triangular matrix.     

Fixed-order H 2 controller design for state space polytopic systems

In this article, the problem of fixed-order H ₂ controller design for continuous-time polytopic systems is investigated. It is assumed that the uncertain parameters appear in the state space realization of the system. A convex set of fixed-order H ₂ controllers is presented by introducing a slack matrix variable which decouples the Lyapunov variables and the controller parameters. Taking advantage of this feature, we can readily design a robust fixed-order controller for a polytopic system with non-common Lyapunov variables. An optimization problem is presented for computing the slack variables using an initial controller selected by the designer. Additionally, to improve the obtained performance, a procedure is provided to reduce the dependency of the method on the initial controller. The design conditions are in terms of solutions to a set of linear matrix inequalities. Numerical examples demonstrate the effectiveness of the proposed approach.     

Toeplitz含噪语音端点鲁棒检测

针对在低信噪比条件下语音端点检测问题,提出了一种基于Toeplitz最大特征值的去噪语音端点检测方法。该方法用语带频谱自相关序列构造一个对称Toeplitz矩阵,利用该矩阵最大特征值的信息量对语音信号进行双门限端点检测。新算法经过实验,能够有效地区分语音和噪声,在不同的低噪声环境条件下具有良好的鲁棒性。与新近的信号递归度分析方法比较,准确率较高。该算法计算代价小,实时性好,简洁易实现。