Multidimensional systems theory and applications /

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...

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Bibliographic Details
Corporate Author:	SpringerLink (Online service)
Other Authors:	Bose, N. K. (Nirmal K.), 1940-, Buchberger, Bruno, Guiver, J. P.
Format:	eBook
Language:	English
Published:	Dordrecht ; Boston : Kluwer Academic Publishers, [2003]
Edition:	Second edition.
Subjects:	System analysis. Mehrdimensionales System. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

1. Trends in Multidimensional Systems Theory 1
2 Multidimensional Systems Stability 2
2.1 Multidimensional Digital Filters 3
2.2 Multivariate Networks 9
2.3 Delay-Differential Systems 12
2.4 Stiff Differential Systems 13
2.5 Multipass Processes 15
3 Multivariate Realization Theory 15
3.1 State-space Realization Theory 16
3.2 Transform Domain Realization Theory 18
3.2.1 Integral Representation of Positive Real Functions 20
3.2.2 Sum of Squares Representation of a Form in Network Synthesis 22
4 n-D Problem of Moments and Its Applications in Multidimensional Systems Theory 23
5 Role of Irreducible Polynomials in Multidimensional Systems Theory 26
6 Hilbert Transform and Spectral Factorization 27
8 Updates 30
2. Causal and Weakly Causal 2-D Filters with Applications in Stabilization 35
1 Scalar 2-D Input / Output Systems 35
2 Stability 38
3 Structural Stability 43
4 Multi-Input Multi-Output Systems 43
5 Stabilization of Scalar Systems 44
6 Characterization of Stabilizers for Scalar Systems 47
7 Stabilization of Strictly Causal Transfer Matrices 53
7.1 MIMO Feedback Systems and Their Stabilization 55
8 Characterization of Stabilizers for MIMO Systems 59
9 Stabilization of Weakly Causal Systems 63
10 Stabilization of MIMO Weakly Causal Systems 73
12 Updates 77
3. The Equation Ax = b Over the Ring C[z, w] 79
2 Sufficient Condition For Solution 79
3 Appendix A. Zero-Dimensional Polynomial Ideals 86
4. Grobner Bases: An Algorithmic Method in Polynomial Ideal Theory 89
2 Grobner Bases 91
3 Algorithmic Construction of Grobner Bases 95
4 An Improved Version of the Algorithm 98
5 Application: Canonical Simplification, Decision Of Ideal Congruence And Membership, Computation In Residue Class Rings 103
6 Application: Solvability and Exact Solution of Systems of Algebraic Equations 108
7 Application: Solution of Linear Homogeneous Equations With Polynomial Coefficients 116
8 Grobner Bases For Polynomial Ideals Over The Integers 120
9 Other Applications 124
10 Specializations, Generalizations, Implementations, Complexity 125
11 Updates 126
5. Multivariate Polynomials, Matrices, and Matrix-Fraction Descriptions 129
2 Relative Primeness and GCD Extraction from Multivariate Polynomials 131
2.1 Tests for Relative Primeness 131
2.2 Primitive factorization algorithms for GCD extraction 133
2.2.1 Multivariate GCD extraction from the Sylvester matrix 133
2.3 Bezout Matrix Based Method 135
2.3.1 Multivariate Polynomial GCD Extraction from Bezout Matrix 136
3 Polynomial Matrix Primitive Factorization in the Bivariate Case 138
3.1 Primitive Factorization of Bivariate Polynomial Matrices 140
3.2 General Factorization of Bivariate Polynomial Matrices 147
4 Multivariate Polynomial Matrix Factorization 151
4.1 Various Types of Multivariate Polynomial Matrix Factorizations 151
4.2 Modules 151
4.3 Various Degrees of Primeness 155
4.4 R-Modules and Vector Spaces 159
5 Computations for Coprimeness Using Grobner Bases 161
5.1 Algorithm for Computing the Right Inverse of ZLC Matrices 162
5.2 Minor coprimeness and Grobner Bases 163
5.3 Problems in Factor Coprimeness and GCLD (GCRD) Extraction 168
6 Generalization of the Serre Conjecture and its Consequences 170
6.1 Normal Full Rank Matrix Case 170
6.1.1 Factorization Problem in Normal Full Rank Case 174
6.2 Degenerate Rank Case 174
7 Factorization as a Product of Elementary Matrix Factors 176
8 Applications in Multidimensional Systems Stabilization 178
9 Behavioral Approach 184
6. Recent Impacts of Multidimensional Systems Research 191
2 Inference of Stability of Sets of Multidimensional Systems From Subsets of Low Cardinality 192
2.1 Univariate Complex Hurwitz Polynomial Case 192
2.2 Multivariate Scattering Hurwitz Polynomial Case 193
2.3 Robust Wavenumber Response 198
2.4 Stability Of Interval Matrix 199
3 Multiple Deconvolution Operators for Robust Superresolution 200
3.1 Recursive Least Squares (RLS) Algorithm for Superresolution 202
3.2 Backprojection Algorithm for Superresolution 206
4 Multisensor Array-Based Superresolution 207
4.1 Multisensor High Resolution Image Reconstruction Model 209
4.2 Regularization Methods 211
5 Wavelets for Superresolution 213
6 Other Recent Applications 216
7. Multivariate Rational Approximants of the Pade-Type 221
1 Introduction and Motivation 221
2 Multivariate Pade-Type Approximants (Scalar Case) 222
3 Pade-Type Matrix Approximants 226
5 Updates 228
8. Old Problem Solutions and Some New Problems 231
1 Progress Towards Solution of Open Problems since 1985 231
1.1 Nonessential Singularities of the Second Kind (NSSK) 231
1.2 Rational Spectral Factorization 232
1.3 Feedback Stabilization 233
1.4 Robust Continuous System Stability 235
1.5 Stability of Discrete Systems Under Coefficient Perturbation 236
1.6 Robust Stability of Multivariable Systems 237
2 New Open Problems 238
2.1 Greatest Common Left (Right) Divisor Computation 238
2.2 Determinantal (Left Right Joint) Factorization 239
2.3 Unimodular Completion Over Ring of Proper Stable Multivariate Rational Functions 240
2.4 Minimax Controller and Grobner Bases 242.