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| Tannenbaum A. — Invariance and System Theory: Algebraic and Geometric Aspects |
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| Предметный указатель |
Absolutely minimal realization 93
Affine variety 1 97
Algebraic group 36
Algebraic group, geometrically reductive 46
Algebraic group, linear 37
Algebraic group, linearly reductive 44
Algebraic group, radical of 45
Algebraic group, reductive 46
Algebraic observability 99
Algebraically canonical system 100
Associated sheaf 11
Blending problem 136
Braid group 110
Brunovsky canonical form 123
Canonical realization 33 91
Canonical system 33 91
Cauchy index 105
Causality 100
Cech cocycle 12
Coarse moduli space 39
Cocycle condition 12 14
Coefficient assignability 130
Concatenation 19 78
Connection 28
Constant sheaf 11
Constructibility 24
Constructible set 9
Control canonical form 27 69
Controllability 22
Coordinate ring 6
Covariant differential operator 28
Covering space 109
Cyclic section 30
Differential equation of order n 29—30
Differential equation of order n, solution of 30
Dimension of variety 8
Divisor 113
Dual bundle 12
Dual system 93
Dynamic output feedback 133
Dynamical system 18
Dynamical system in input/output or external sense 19
Dynamical system, constant 21
Dynamical system, continuous 20
Dynamical system, discrete 20
Dynamical system, finite dimensional 21
Dynamical system, linear 20
Dynamical system, smooth 20
Dynamical system, time-invariant 21
Equilibrium point 97 119
Equilibrium point, asymptotically stable 120
Equilibrium point, stable 120
Event space 19
Family of deformations 67
Family of endomorphisms 38
Family of systems 55 63 89
Fatou ring 92
Feedback equivalence 126
Field of definition 16
Fine moduli space 39
Free system 26
Fuhrmann realization 86
Function field 8
Fundamental group 109
Gain factor 143
Gain matrix 133
Geometric quotient 44
Geometric quotient, universal 62
Graded ring 4
Grassmann variety 14
Hankel matrix 81 91
Hermann — Martin bundle 125
Hermann — Martin map 124
Hilbert's 14th problem 45
Homogeneous coordinate ring 7
Homogeneous coordinates 4
Homogenized pencil 125
Homotopy 108
Horizontal section 28
Hurwitz polynomial 120
Identification theory 104
Iitpulse/response sequence 81
Impulse/response function 34
Input function 18
Input values 18
Input/output map 19
Input/output map, constant causal 100
Input/output map, discrete time constant linear 77
Input/output map, polynomial 101
Interlacing property 144
Irreducible 2
Jacobson radical 96
Jump point 89
k-ideal 96
K-rational point 16
k-topology 17
Kalman realization 79
Kronecker indices 68
Kronecker nice selection 68
| Laplace transform 32
Left coprime factorization 85
Length of input sequence 77
Local holomorphic canonical form 67
Local moduli space 67
Local system 28
Locally closed 9
Loop space 115
Lyapunov function 121
McMillan degree 33 107
Minimal partial realization 87
Minimal realization 80
Morphism 6 97
Morphism, dominating 103
Morphism, projective 53
Mumford conjecture 46
n-th homotopy group 109
Nerode equivalence 78
Nevanlinna interpolation 139—142
Nevanlinna-Pick matrix 142
Nice selection 52
Nilradical 96
Observability 25 91 99
Observation algebra 99
Output feedback transformation 133
Output functions 18
Output values 18
Pade approximation 87
Partial Hankel matrix 88
Partial realization 76 87
Pencil of matrices 125
Pluecker map 15
Pole assignability 130
Polynomial response map 101
Polynomial system 97
Pre-stable point 52
Presheaf 10
Principal bundle 15
Projective space 3
Projective variety 4
Quasi-affine variety 2
Quasi-projective variety 4
Quasi-reachability 98
Quotient 43
r-jet 29
Radical 2 97
Rational action 44
Rational canonical form 27
Rational function 8
Reachability 22 91 98
Readout map 19
Realization 19 33 35 77 81 84 91 102
Reduced k-algebra 11 97
Regular map 6 97
Relative homotopy group 110
Representable functor 39
Residue 86
Response map 101
Richardson's criterion 46
Riemann surface 28
Right coprime factorization 85
Routh criterion 120
Scheme 3 97
Section 10 13
Serre conjecture 13
Sheaf 10
Sheaf of modules 11
Sheaf, locally free 11
Shift operator 21 77 86
Signature 106
Split family 95
Split system 93
Stalk 10
State feedback 122
State module 90
State set 18
State space form 26
State transition function 19
Stein space 137
Strict equivalence 127
Structure sheaf 10
System over a ring 21 90
Tangent space 12
time set 18
Transfer function 33
Transfer function, strictly proper 33 84
Transition matrix 25
Unimodular 85
Universal bundle 60
Universal covering 110
Universal family 55
Universal quotient bundle 61
Universal subbundle 61
Vector bundle 11
Vector bundle, fiber of 12
Vector bundle, trivial 13
Versal family of deformations 67
Versal morphism 66
Volterra series 100
Zariski topology 1 5 97
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