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31
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and mat ..."
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Cited by 74 (0 self)
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A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
DStability of Polynomial Matrices
, 1999
"... Necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region D of the complex plane. The conditions stem from a general optimization methodology mixing LFRs, rankone LMIs and the Sprocedure. They are expressed as an LMI feasibility ..."
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Cited by 13 (12 self)
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Necessary and sufficient conditions are formulated for the zeros of an arbitrary polynomial matrix to belong to a given region D of the complex plane. The conditions stem from a general optimization methodology mixing LFRs, rankone LMIs and the Sprocedure. They are expressed as an LMI feasibility problem that can be tackled with widespread powerful interiorpoint methods. Most importantly, the Dstability conditions can be combined with other LMI conditions arising in robust stability analysis. Keywords Polynomial Matrix, Dstability, LMI. 1 Introduction Polynomial matrices play a central role in modern systems theory. Algebraic methods such as the polynomial approach [23] or the behavioral approach [35] heavily rely upon polynomial matrices. Unsurprisingly, fundamental system features are captured by properties of polynomial matrices. For example, the zeros of the denominator polynomial matrix in a matrix fraction description [22] characterize system dynamics and performance. Sat...
Multiple model adaptive control, part 1: Finite controller coverings
 Int. J. Robust Nonlinear Control
, 2000
"... We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear timeinvariant plant models, it is possible to determine a finite set ..."
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Cited by 12 (8 self)
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We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear timeinvariant plant models, it is possible to determine a finite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the finite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately band and timelimited transfer functions is approximately finitedimensional.
Improved Polynomial Matrix Determinant Computation
, 1999
"... An early result on the SmithMacMillan form of a rational matrix is used for evaluating the degree of the determinant of a polynomial matrix using numerically reliable techniques. This allows for accurate determinant zeroing and determinant interpolation, thus improving existing numerical methods fo ..."
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Cited by 6 (4 self)
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An early result on the SmithMacMillan form of a rational matrix is used for evaluating the degree of the determinant of a polynomial matrix using numerically reliable techniques. This allows for accurate determinant zeroing and determinant interpolation, thus improving existing numerical methods for polynomial matrix determinant computation. Keywords Polynomial Matrix, Determinant Computation, Numerical Methods. 1 Motivation As pointed out in [4], one of the main stumbling block when designing algorithms for numerical computation of the determinant d(s) = d 0 + d 1 s + \Delta \Delta \Delta + d ffi s ffi of a given nonsingular n \Theta n polynomial matrix A(s) = A 0 +A 1 s + \Delta \Delta \Delta +A ff s ff is the correct evaluation of the degree ffi. This work was supported by the Barrande Project No. 97/00597/026, by the Grant Agency of the Czech Republic under contract No. 102/99/1368 and by the Ministry of Education of the Czech Republic under contract No. VS97/034. y Co...
A Toeplitz algorithm for the polynomial Jspectral factorization
 IFAC Symposium on System, Structure and Control
, 2004
"... A block Toeplitz algorithm is proposed to perform the Jspectral factorization of a paraHermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given a ..."
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Cited by 6 (3 self)
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A block Toeplitz algorithm is proposed to perform the Jspectral factorization of a paraHermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation of the nullspaces of related block Toeplitz matrices, polynomial matrix factor extraction and linear polynomial matrix equations solving.
Fundamental Equivalence of DiscreteTime AR Representations
 INTERNAT. J. CONTROL
, 2001
"... We examine the problem of equivalence of discrete time autoregressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0, N ] if their solution spaces or behaviours are isomorphic. We generalise the concept o ..."
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Cited by 6 (4 self)
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We examine the problem of equivalence of discrete time autoregressive representations (DTARRs) over a finite time interval. Two DTARRs are defined as fundamentally equivalent (FE) over a finite time interval [0, N ] if their solution spaces or behaviours are isomorphic. We generalise the concept of strict equivalence (SE) of matrix pencils to the case of general polynomial matrices and in turn we show that FE of DTARRs implies SE of the underlying polynomial matrices.
A Spectral Characterization Of The Behavior Of Discrete Time ARRepresentations Over A Finite Time Interval
"... In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the ARequation. A boundary mapping equation and a closed formula for the d ..."
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Cited by 5 (4 self)
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In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the ARequation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also given.
Numerical computation of minimal polynomial bases: A generalized resultant approach
 Linear Algebra Appl
"... We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal ..."
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Cited by 5 (0 self)
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We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F (s): The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coe ¢ cients.
Cost of Cheap Decoupled Control
 IEEE CDC
, 1998
"... It is known that requiring a controlled system to be decoupled may increase costs in terms of some performance measures. However, decoupling may be desirable from an applied perspective. This paper gives an explicit quantification of the costs of decoupling. In particular, the average quadratic trac ..."
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Cited by 4 (3 self)
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It is known that requiring a controlled system to be decoupled may increase costs in terms of some performance measures. However, decoupling may be desirable from an applied perspective. This paper gives an explicit quantification of the costs of decoupling. In particular, the average quadratic tracking error is used to quantify performance. The analysis exploits the parametrisation of all decoupling controllers, together with WienerHopf frequency domain techniques. The results allow rational choices to be made about the relative desirability of decoupling for particular applications. Key Phrases Limiting H 2 costs, Output Decoupling, StateFeedback, Output Feedback, Optimisation, WienerHopf. 1 Introduction A central issue in filtering and control is that of fundamental performance limits. Work in this area has a long history beginning with the seminal work of Bode [1]. The available results can be broadly classified into three categories, namely; 1. Frequency domain integrals on ...
Comparison of Algorithms for Computing Infinite Structural Indices of Polynomial Matrices
, 2002
"... A new algorithm is proposed to compute the infinite structural indices of a polynomial matrix, i.e. the algebraic and geometric multiplicities of its poles and zeros at infinity. Infinite structural indices of polynomial matrices play a key role when solving e.g. multivariable decoupling control pro ..."
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Cited by 4 (2 self)
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A new algorithm is proposed to compute the infinite structural indices of a polynomial matrix, i.e. the algebraic and geometric multiplicities of its poles and zeros at infinity. Infinite structural indices of polynomial matrices play a key role when solving e.g. multivariable decoupling control problems. The algorithm is based on numerically stable operations only, and takes full advantage of the block Toeplitz structure of a constant matrix built directly from the polynomial matrix coefficients. Comparative numerical examples and a full computational complexity analysis indicate that the Toeplitz algorithm can be viewed as a competitive alternative to the wellknown statespace pencil matrix algorithm for obtaining structural indices.