Topics in Multidimensional Linear Systems TheorySpringer Science & Business Media, 16 Ağu 2000 - 164 sayfa The past few decades have witnessed an increasing interest in the field of multidimensional systems theory. This is concerned with systems whose trajectories depend not on one single variable (usually interpreted as time or frequency), but on several independent variables, such as the coordinates of an image. The behavioural approach introduced by J. C. Willems provides a particularly suitable framework for developing a linear systems theory in several variables. The book deals with the classical concepts of autonomy, controllability, observability, and stabilizability. All the tests and criteria given are constructive in the sense that algorithmic versions may be implemented in modern computer algebra systems, using Gröbner basis techniques. There is a close connection between multidimensional systems theory and robust control of one-dimensional systems with several uncertain parameters. The central link consists in the basic tool of linear fractional transformations. The book concludes with examples from the theory of electrical networks. |
İçindekiler
I | 1 |
II | 2 |
III | 3 |
IV | 4 |
V | 5 |
VI | 7 |
VII | 11 |
VIII | 14 |
XXIX | 71 |
XXX | 73 |
XXXI | 77 |
XXXII | 85 |
XXXIII | 86 |
XXXIV | 89 |
XXXV | 101 |
XXXVI | 105 |
IX | 15 |
X | 18 |
XI | 22 |
XIII | 26 |
XIV | 32 |
XV | 33 |
XVII | 34 |
XVIII | 41 |
XIX | 42 |
XX | 44 |
XXI | 45 |
XXII | 47 |
XXIII | 49 |
XXIV | 52 |
XXV | 57 |
XXVII | 64 |
XXVIII | 69 |
XXXVII | 108 |
XXXVIII | 114 |
XXXIX | 118 |
XL | 121 |
XLI | 125 |
XLII | 127 |
XLIII | 133 |
XLIV | 137 |
XLV | 141 |
XLVI | 142 |
XLVII | 143 |
XLVIII | 145 |
XLIX | 150 |
L | 157 |
163 | |
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
admissible system algebraic arbitrary B₁ B₂ behavior block matrix co-dimension coefficient matrix compute consider controllability controllable(4 Corollary corresponding D-module defined Definition denotes determinantal ideals dimension DV representation equations exists factorization of H finite FSSE full column rank full row rank GFLP given greatest common divisor Gröbner basis hence image representation implies invertible ker(R kernel representation matrix Knxn Laurent polynomial left co-prime factorization left factor Lemma linear fractional transformation M₁ minimal left annihilator minimal right annihilator minor primeness module multidimensional systems multivariate n₁ nodal analysis non-singular notion p₁ parameter partition permutation matrix polynomial matrix polynomial ring Proof R₁ rational functions rational matrix right co-prime factorization right factorization sequence signal domain stability radius T₁ T₂ Theorem transfer function unimodular V₁ variables vector vertex w₁ W₂ zero left prime zero right co-prime zero right prime