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inner-outer factorization and the inversion of locally finite systems of equations

LINEAR ALGEBRA AND ITS APPLICATIONS 2000年第1-3期313卷 53-100页

作者： Dewilde, P van der Veen, AJ Delft Univ Technol DIMES NL-2600 GA Delft Netherlands

We consider the problem of computing the inverse of a large class of infinite systems of linear equations, which are described by a finite set of data. The class consists of equations in which the linear operator is represented by a discrete time-varying dynamical system whose local state space is of finite dimension at each time point k, and which reduces to time invariant systems for time points k --> +/-infinity. In this generalization of classical matrix inversion theory, inner-outer factorizations of operators play the role that QR-factorization plays in classical linear algebra. Numerically, they lead to so-called 'square root' implementations, for which am-active algorithms can be derived, which do not require the determination of spurious multiple eigenvalues, as would be the case if the problem was converted to a discrete time Riccati equation by squaring. We give an overview of the theory and the derivation of the main algorithms. The theory contains both the standard LTI case and the case of a finite set of linear equations as special instances, a particularly instance of which is called 'matrices of low Hanker rank', recently sometimes called 'quasi-separable matrices'. However, in the general case considered here, new phenomena occur which are not observed in these classical cases, namely the occurrence of 'defect spaces'. We describe these and give an algorithm to compute them as well. In all cases, the algorithms given are linear in the amount of data. (C) 2000 Elsevier Science Inc. All rights reserved.

关键词： inner-outer factorization URV decomposition QR factorization square-root algorithm Riccati equation Lyapunov-Stein equation system inversion time-varying systems quasi-separable matrices doubling algorithm

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inner-outer factorization for strictly proper transfer matrices

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2002年第11期47卷 1915-1919页

作者： Gu, GX Louisiana State Univ. Baton Rouge

This note considers inner-outer factorization for strictly proper transfer matrices. We provide characterizations to the solution of this particular factorization problem, and develop a computational algorithm to solv... 详细信息

关键词： inner-outer factorization linear quadratic regulator (LQR) singular systems

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inner-outer factorization of discrete-time transfer function matrices

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 1996年第11期43卷 941-945页

作者： Lin, ZL Chen, BM Saberi, A Shamash, Y NATL UNIV SINGAPORE DEPT ELECT ENGN SINGAPORE 117548 SINGAPORE WASHINGTON STATE UNIV SCH ELECT ENGN & COMP SCI PULLMAN WA 99164 USA SUNY STONY BROOK COLL ENGN & APPL SCI STONY BROOK NY 11794 USA

The inner-outer factorization of the transfer function matrix of a linear time-invariant system has been an important algebraic problem in a variety of areas in electrical engineering, including systems and control analysis and design. This paper gives an explicit state space-based algorithm for the inner-outer factorization of the transfer function matrix of a general discrete-time linear system. More specifically, the algorithm applies to any discrete-time linear system whose transfer function is proper and stable.

关键词： control system analysis discrete time systems input-output stability linear systems state-space methods transfer function matrices control analysis discrete-time transfer function matrices inner-outer factorization linear time-invariant system stable tra factorization Control system analysis discrete time systems input-output stability Linear system transfer function matrices Time invariant systems discrete-time TRANSFER FUNCTIONS State-space methods

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inner - outer factorization FOR STRICTLY PROPER FUNCTIONS WITH JW-AXIS ZEROS

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SYSTEMS & CONTROL LETTERS 1991年第3期16卷 179-185页

作者： HARA, S SUGIE, T TOKYO INST TECHNOL DEPT CONTROL ENGNMEGURO KUTOKYO 152JAPAN KYOTO UNIV DIV APPL SYST SCIUJIKYOTO 611JAPAN UNIV WATERLOO DEPT ELECT ENGNWATERLOO N2L 3G1ONTARIOCANADA

This paper discussed the inner-outer factorization for square real rational matrices which may have zeros on the j-omega-axis including infinity. A factorization method is given in terms of the descriptor form representation of the rational matrix. This method uses the solution of a generalized Riccati equation. We also propose an efficient computation algorithm for solving the generalized Riccati equation.

关键词： inner-outer factorization DESCRIPTOR FORM REPRESENTATION RICCATI EQUATION GENERALIZED EIGENVALUE PROBLEM JW-AXIS ZERO

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inner-outer factorization for nonlinear noninvertible systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2004年第4期49卷 483-492页

作者： Ball, JA Petersen, MA van der Schaft, A Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA Potchefstroom Univ Christian Higher Educ Dept Math ZA-6001 Potchefstroom South Africa Univ Twente Dept Math Appl NL-7500 AE Enschede Netherlands

This paper considers inner-outer factorization of asymptotically stable nonlinear state space systems in continuous time that are noninvertible. Our approach will be via a nonlinear analogue of spectral factorization which concentrates on first finding the outer factor instead of them inner factor. An application of the main result to control of nonminimum phase nonlinear systems is indicated.

关键词： Hamilton-Jacobi inequality inner-outer factorization nonlinear noninvertible systems nonlinear Smith predictor

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A simple derivation of the right interactor for a tall transfer function matrix and its application to inner-outer factorization

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ELECTRONICS AND COMMUNICATIONS IN JAPAN 2012年第8期95卷 17-25页

作者： Kase, Wataru Osaka Inst Technol Dept Elect & Elect Syst Engn Osaka Japan

The interactor matrix plays several important roles in control systems theory. In this paper, we present a simple method of deriving a right interactor for tall transfer function matrices using the Moore-Penrose pseudoinverse. As a result of the presented method, all zeros of the interactor lie at the origin. The method will be applied to inner-outer factorization for strictly proper transfer function matrices. It will be shown that the stability of the interactor is necessary to calculate the factorization. (c) 2012 Wiley Periodicals, Inc. Electron Comm Jpn, 95(8): 17-25, 2012;Published online in Wiley Online Library (). DOI 10.1002/ecj.11387

关键词： interactor matrix inner-outer factorization strictly proper plant discrete-time systems

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FILTER DESIGN VIA inner-outer factorization - COMMENTS ON OPTIMAL DECONVOLUTION FILTER DESIGN BASED ON ORTHOGONAL PRINCIPLE

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SIGNAL PROCESSING 1994年第1期35卷 51-58页

作者： AHLEN, A STERNAD, M Systems and Control Group Department of Technology Uppsala University P.O. Box 27 S-75103 Uppsala Sweden

This paper is written with two purposes in mind. First, it points out some mistakes made in the paper ''Optimal deconvolution filter design based on orthogonal principle'', recentry published in this journal. Secondly, in order to sort out the reason for those mistakes, the relations between inner-outer factorization, spectral factorization, whitening filters and Diophantine equations in minimum mean square error (MMSE) filter design are stressed. It is emphasized that computation of an inner matrix corresponds to performing a spectral factorization and the inverse of the outer matrix is a whitening filter. Furthermore, finding the causal part of an expression is the same as solving a Diophantine equation.

关键词： DECONVOLUTION inner-outer factorization WIENER FILTERS FILTER DESIGN

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Robustness of the inner-outer factorization and of the spectral factorization for FIR data

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第1期56卷 274-283页

作者： Boche, Holger Pohl, Volker Tech Univ Berlin Heinrich Hertz Chair Mobile Commun D-10587 Berlin Germany Heinrich Hertz Inst Nachrichtentech Berlin GmbH Fraunhofer Inst Telecommun D-10587 Berlin Germany German Sino Mobile Commun Lab D-10587 Berlin Germany

The present paper analyzes the construction of outer functions, the factorization of finite-impulse response (FIR) systems into a minimum phase system and an all-pass part, and the spectral factorization. It investigates the behavior of these operations with respect to errors in the given data. It shows that the error in the constructed outer function grows at least and at most proportional with the logarithm of the degree of the given FIR system and proportional to the error in the given data. For the other two operations, it turns out that they show the same behavior with respect to errors in the given FIR data as the construction of outer functions.

关键词： construction of minimum phase system dimensional effects error bounds inner-outer factorization robustness spectral factorization

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Identifying an autoregressive process disturbed by a moving-average noise using inner-outer factorization

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SIGNAL IMAGE AND VIDEO PROCESSING 2015年第1-Sup期9卷 235-244页

作者： Abdou, Ahmed Turcu, Flavius Grivel, Eric Diversi, Roberto Ferre, Guillaume Al Quds Univ Dept Elect & Commun Engn Jerusalem Israel Univ Bordeaux UMR CNRS 5218 Bordeaux INP ENSEIRB MATMECA IMS Cours Liberat 351 F-33405 Talence France Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

This paper deals with the identification of an autoregressive (AR) process disturbed by an additive moving-average (MA) noise. Our approach operates as follows: Firstly, the AR parameters are estimated by using the overdetermined high-order Yule-Walker equations. The variance of the AR process driving process can be deduced by means of an orthogonal projection between two types of estimates of AR process correlation vectors. Then, the correlation sequence of the MA noise is estimated. Secondly, the MA parameters are obtained by using inner-outer factorization. To study the relevance of the resulting method, we compare it with existing algorithms, and we analyze the identifiability limits. The identification approach is then combined with Kalman filtering for channel estimation in mobile communication systems.

关键词： Autoregressive process (AR) Moving-avergae process (MA) inner-outer factorization Overdetermined high-order Yule-Walker equations

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Rayleigh fading channel simulator based on inner-outer factorization

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SIGNAL PROCESSING 2010年第1期90卷 24-33页

作者： Merchan, Fernando Turcu, Flavius Grivel, Eric Najim, Mohamed Univ Bordeaux 1 Dept LAPS IMS F-33405 Talence France

The paper deals with the design of Rayleigh fading channel simulators based on the inner-outer factorization. The core of the approach is to approximate the outer spectral factor of the channel power spectral density (PSD) by either finite-order polynomials or rational functions. This, respectively, leads to MA or AR/ARMA models. The parameter estimation operates in two steps: the outer factor, which leads to a minimum-phase filter, is first evaluated inside the unit disk of the z-plane. Then, we propose to compute the Taylor expansion coefficients of the outer factor because they coincide with the model parameters. Unlike other simulation techniques, this has the advantage that the first p parameters remain unchanged when one increases the model order from p to p+1. A comparative study with existing channel simulation approaches points out the relevance of our ARMA model-based method. Moreover, the ARMA model weakens the oscillatory deviations from the theoretical PSD in the case of AR models, or low peaks at the Doppler frequencies for MA models. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Moving average processes Autoregressive processes Autoregressive moving average processes Rayleigh fading channel inner-outer factorization

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