Multidimensional Systems Theory and Applications / Edition 2

Multidimensional Systems Theory and Applications / Edition 2

by N.K. Bose
     
 

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ISBN-10: 1402016239

ISBN-13: 9781402016233

Pub. Date: 11/30/2003

Publisher: Springer Netherlands

This second edition brings the reader on par with the flurry of research results generated during the last two decades in the theory and applications of multidimensional systems. This book has an abundance of examples to illustrate advanced concepts and brings out, for the first time, in a text book setting the algorithms for bivariate polynomial matrix

Overview

This second edition brings the reader on par with the flurry of research results generated during the last two decades in the theory and applications of multidimensional systems. This book has an abundance of examples to illustrate advanced concepts and brings out, for the first time, in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. The reader is alerted to the reasons for the difficulties in generalization to the higher dimensional case. Algorithms and their implementation using symbolic algebra are emphasized.

Product Details

ISBN-13:
9781402016233
Publisher:
Springer Netherlands
Publication date:
11/30/2003
Edition description:
2nd ed. 1995
Pages:
269
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

List of Acronymsxi
List of Notationsxii
Prefacexiii
Acknowledgmentsxvii
Introductionxix
1.Trends in Multidimensional Systems Theory1
1Introduction1
2Multidimensional Systems Stability2
2.1Multidimensional Digital Filters3
2.2Multivariate Networks9
2.3Delay-Differential Systems12
2.4Stiff Differential Systems13
2.5Multipass Processes15
3Multivariate Realization Theory15
3.1State-space Realization Theory16
3.2Transform Domain Realization Theory18
3.2.1Integral Representation of Positive Real Functions20
3.2.2Sum of Squares Representation of a Form in Network Synthesis22
4n-D Problem of Moments and Its Applications in Multidimensional Systems Theory23
5Role of Irreducible Polynomials in Multidimensional Systems Theory26
6Hilbert Transform and Spectral Factorization27
7Conclusions28
8Updates30
2.Causal and Weakly Causal 2-D Filters with Applications in Stabilization35
1Scalar 2-D Input / Output Systems35
2Stability38
3Structural Stability43
4Multi-Input Multi-Output Systems43
5Stabilization of Scalar Systems44
6Characterization of Stabilizers for Scalar Systems47
7Stabilization of Strictly Causal Transfer Matrices53
7.1MIMO Feedback Systems and Their Stabilization55
8Characterization of Stabilizers for MIMO Systems59
9Stabilization of Weakly Causal Systems63
10Stabilization of MIMO Weakly Causal Systems73
11Conclusions77
12Updates77
3.The Equation Ax = b Over the Ring C[z, w]79
1Introduction79
2Sufficient Condition For Solution79
3Appendix A. Zero-Dimensional Polynomial Ideals86
4.Grobner Bases: An Algorithmic Method in Polynomial Ideal Theory89
1Introduction89
2Grobner Bases91
3Algorithmic Construction of Grobner Bases95
4An Improved Version of the Algorithm98
5Application: Canonical Simplification, Decision Of Ideal Congruence And Membership, Computation In Residue Class Rings103
6Application: Solvability and Exact Solution of Systems of Algebraic Equations108
7Application: Solution of Linear Homogeneous Equations With Polynomial Coefficients116
8Grobner Bases For Polynomial Ideals Over The Integers120
9Other Applications124
10Specializations, Generalizations, Implementations, Complexity125
11Updates126
5.Multivariate Polynomials, Matrices, and Matrix-Fraction Descriptions129
1Introduction129
2Relative Primeness and GCD Extraction from Multivariate Polynomials131
2.1Tests for Relative Primeness131
2.2Primitive factorization algorithms for GCD extraction133
2.2.1Multivariate GCD extraction from the Sylvester matrix133
2.3Bezout Matrix Based Method135
2.3.1Multivariate Polynomial GCD Extraction from Bezout Matrix136
3Polynomial Matrix Primitive Factorization in the Bivariate Case138
3.1Primitive Factorization of Bivariate Polynomial Matrices140
3.2General Factorization of Bivariate Polynomial Matrices147
4Multivariate Polynomial Matrix Factorization151
4.1Various Types of Multivariate Polynomial Matrix Factorizations151
4.2Modules151
4.3Various Degrees of Primeness155
4.4R-Modules and Vector Spaces159
5Computations for Coprimeness Using Grobner Bases161
5.1Algorithm for Computing the Right Inverse of ZLC Matrices162
5.2Minor coprimeness and Grobner Bases163
5.3Problems in Factor Coprimeness and GCLD (GCRD) Extraction168
6Generalization of the Serre Conjecture and its Consequences170
6.1Normal Full Rank Matrix Case170
6.1.1Factorization Problem in Normal Full Rank Case174
6.2Degenerate Rank Case174
7Factorization as a Product of Elementary Matrix Factors176
8Applications in Multidimensional Systems Stabilization178
9Behavioral Approach184
10Conclusions187
6.Recent Impacts of Multidimensional Systems Research191
1Introduction191
2Inference of Stability of Sets of Multidimensional Systems From Subsets of Low Cardinality192
2.1Univariate Complex Hurwitz Polynomial Case192
2.2Multivariate Scattering Hurwitz Polynomial Case193
2.3Robust Wavenumber Response198
2.4Stability Of Interval Matrix199
3Multiple Deconvolution Operators for Robust Superresolution200
3.1Recursive Least Squares (RLS) Algorithm for Superresolution202
3.2Backprojection Algorithm for Superresolution206
4Multisensor Array-Based Superresolution207
4.1Multisensor High Resolution Image Reconstruction Model209
4.2Regularization Methods211
5Wavelets for Superresolution213
6Other Recent Applications216
7Conclusions218
7.Multivariate Rational Approximants of the Pade-Type221
1Introduction and Motivation221
2Multivariate Pade-Type Approximants (Scalar Case)222
3Pade-Type Matrix Approximants226
4Conclusions227
5Updates228
8.Old Problem Solutions and Some New Problems231
1Progress Towards Solution of Open Problems since 1985231
1.1Nonessential Singularities of the Second Kind (NSSK)231
1.2Rational Spectral Factorization232
1.3Feedback Stabilization233
1.4Robust Continuous System Stability235
1.5Stability of Discrete Systems Under Coefficient Perturbation236
1.6Robust Stability of Multivariable Systems237
2New Open Problems238
2.1Greatest Common Left (Right) Divisor Computation238
2.2Determinantal (Left Right Joint) Factorization239
2.3Unimodular Completion Over Ring of Proper Stable Multivariate Rational Functions240
2.4Minimax Controller and Grobner Bases242
References243
Index265

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