Hinrichsen D., Pritchard A. — Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness :: Электронная библиотека попечительского совета мехмата МГУ

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Hinrichsen D., Pritchard A. — Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness

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Название: Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness

Авторы: Hinrichsen D., Pritchard A.

Аннотация:

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to the analysis of dynamical systems, whereas the second volume will be devoted to control. It combines features of a detailed introductory textbook with that of a reference source. The book contains many examples and figures illustrating the text which help to bring out the intuitive ideas behind the mathematical constructions. It is accessible to mathematics students after two years of mathematics and graduate engineering students specializing in mathematical systems theory. The reader is gradually brought to the frontiers of research and on the way the required mathematical background material is developed with detailed proofs. As such the book will be useful for established researchers in systems theory as well as those just beginning in the field.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 817

Добавлена в каталог: 16.02.2014

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Предметный указатель

$\mu$ -value      450 550 586
$\mu$ -value, block-diagonal perturbations      456
$\mu$ -value, bounds, lower      454
$\mu$ -value, bounds, upper      452
$\mu$ -value, complex structures, characterization      453
$\mu$ -value, complex structures, continuity      465
$\mu$ -value, diagonal perturbations upper bound      458
$\mu$ -value, full-block perturbations, complex, characterization      454
$\mu$ -value, full-block perturbations, complex, of minimum norm      454
$\mu$ -value, full-block perturbations, real, characterization q or l=1      467
$\mu$ -value, full-block perturbations, real, characterization q, $l\geq 2$       474
$\mu$ -value, full-block perturbations, real, continuity      477
$\mu$ -value, full-block perturbations, real, Lipschitz continuity      478
$\mu$ -value, full-block perturbations, real, upper semicontinuity      466
$\mu$ -value, multi-block perturbations, characterization      459 461 463
$\mu$ -value, multi-block perturbations, upper bound      457 460
$\mu$ -value, properties      452
$\mu$ -value, upper semicontinuity      464
A/D-converter      168
Absolutely continuous      83 740
Aizerman's conjecture      701 712
Aizerman's conjecture, multivariable      702
Aizerman's conjecture, theorem      703
Algebraic stability domains      357
Algorithms for complex stability radius      607
Algorithms for eigenvalues      506—508
Algorithms for eigenvalues, power methods      506
Algorithms for Liapunov equations Bartels — Stewart      512
Algorithms for singular values      508—511
Algorithms for singular values, Golub — Kahan — Reinsch      509
Algorithms, Francis' double-shift QR      502—506
Ampere's law      42
Analytic continuation      380 400 402 733
ARC      297 380 724
Argument      297 725
Argument function      298 725
Argument, change of      297 725 727
Argument, principle of      297 731
Argument, rate of change      298 299
Attractive closed set      211
Attractive equilibrium point      200
Attractive globally      200 695
Attractor      211
Attractor, asymptotically stable      227 240
Automaton      79 80 95 see
Automaton, next-state function      79
Automobile suspension system      16 533
Bandwidth      173
Basin of attraction      223 225 232
Basin of attraction, guaranteed domain of attraction      705
Basin of attraction, of an attractor      211
Basin of attraction, of an equilibrium point      200
Bauer — Fike Lemma      404 524
Bezout matrix      317—320
Bezout matrix, discrete      351
Bidiagonal form      495
Bidiagonal form, algorithm for reducing to      497
Birkhoff's Recurrence Theorem      209
Bohl exponent      258 259 262 278
Bohl transformation      262
Boundary Crossing Theorem      374
Branch point      381 401 419
Branch point, order      401 419
Brockett's Theorem      332
Bromwich contour      670
Butler's Theorem      419
Caratheodory conditions      84
Caratheodory's theorem      84
Cart-pendulum system      23 33 165
Cassini ovals      554 584
Cauchy index      308—312
Cauchy — Schwarz inequality for functions      134 740
Cauchy — Schwarz inequality for sequences      174 735
Cauchy's integral theorem      727
Causality      77 135 687
Cayley transform      268 618
Cayley's problem      211
Characteristic multipliers      266
Cholesky factorization      445 446
Closed curve      310 724
Closed curve, simple      724
Closed graph theorem      757
Closed range theorem      758
Cobweb model      8
Cocycle property      77 196 417
Cohort population model      356
Comparison functions of class $\mathscr{K}$       219 248
Comparison functions of class $\mathscr{K}_{\infty}$       219
Comparison functions of class $\mathscr{LK}$       219 248
Condition number      666 667
Condition number for determining eigenvalues      490
Condition number for determining singular values      491
Condition number for solving Liapunov equations      488
Condition number for solving linear equations      486
Configuration space      29 30
Congruent      314 318 321 723
Conjugate exponent      715
Connected arcwise      387 564 724
Connected components      212 527 545 558—559 563—564 724
Connected components of $Rat_{n}(\mathds{R})$       332
Connected simply      377 559 732
Constraint      27
Constraint, holonomic      29
Continuity equation      43
Contraction      see "Semigroup"
Convergence in norm, uniform, strong, weak      756
Convex combinations of polynomials      640
Convex direction      366 647
Convolution inequality for functions      133 741
Convolution inequality for sequences      149 736
Convolution kernel      127 136
Convolution of functions      126 740
Convolution of sequences      125 736
Convolution system      136
Convolution system, transfer function      147—151
Coulomb's law      40
Coupling matrices      160 161
Courant — Fischer minimax theorem      433
Critical point of a parametrized matrix      400
Critical point of a parametrized polynomial      377
D/A-converter      168
Decreasing along a trajectory      221
Decreasing along a trajectory, strictly      221
Delay system      90 141 710
Delay system, time-varying delay      690
Departure from normality      657
Diagonalizable      399 405 423 723
Differential inclusion      676
Digital systems      56—68
Digital systems, finite state machines      56
Digital systems, finite state machines, latches and flip-flops      62
Digital systems, finite state machines, parity check machine      58 95
Digital systems, finite state machines, realization      69
Digital systems, finite state machines, shift register      80
Digital systems, finite state machines, three bit counter      67
Digital systems, memoryless      56 80
Digital systems, memoryless, half adder, full adder      57
Digital systems, memoryless, logic gates      59 80
Dirac impulse      128 741
Direct sum of matrices      594 720
Direct sum of subspaces, vector spaces      105 720
Direct sum of systems      159 594
Directed graph      50 164—166
Directed graph, cut-set      51
Directed graph, cycle, edge, vertex      50
Directed graph, incidence map      50
Directed graph, strongly connected      51
Discretization methods of order p      185
Discretization methods, Adams — Bashforth      184
Discretization methods, Adams — Bashforth, stability      270

Discretization methods, Euler      178
Discretization methods, Euler, stability      270
Discretization methods, explicit, implicit      182
Discretization methods, Heun      182
Discretization methods, midpoint      183
Discretization methods, midpoint, stability      270
Discretization methods, Milne      185
Discretization methods, Milne, stability      270
Discretization methods, multi-step, single-step      182
Discretization methods, predictor-corrector      182
Discretization methods, Runge — Kutta      183
Discretization methods, Runge — Kutta, stability      270
Discriminant      377
Dissipative      660 661
Dissipative, strictly      660 661
Distance from instability      609 669 672
Distance from instability of a normal matrix      612
Distance from instability of polynomials      630 634 642
Distance from instability, bounds      611 612
Distance from instability, characterizations      610
Distance from instability, under similarity transformations      613
Distance from non-dissipativity      675
Distance from normality      657 669
Distance from singularity      437 474
Domain      376 724
Dyadic decomposition      143
Dynamical system      77
Dynamical system, complete      78
Dynamical system, differentiable      83
Dynamical system, finite      90
Dynamical system, finite dimensional      90
Dynamical system, infinite dimensional      90 115 690
Dynamical system, inputs, outputs      74
Dynamical system, linear      91
Dynamical system, memoryless      56 80
Dynamical system, output map      77
Dynamical system, recursive      88
Dynamical system, reversible      79
Dynamical system, state      75
Dynamical system, state transition map      76
Dynamical system, time-invariant      89 104
Eccentricity      663 676
Eigenbasis, analyticity      416 421
Eigenbasis, analyticity, single real parameter      423
Eigenloci      606
Eigenmode      see "Eigenmotion"
Eigenmotion, complex      106 113
Eigenmotion, complex, generalized      105 113
Eigenmotion, real      107 114
Eigenmotion, real, generalized      107
Eigennilpotents      105 410
Eigennilpotents, analyticity      414
Eigennilpotents, behaviour near a critical point      419
Eigenprojections      105 410
Eigenprojections, analyticity      414 420 421
Eigenprojections, analyticity, single real parameter      422
Eigenprojections, behaviour near a critical point      419
Eigenprojections, total projection      413
Eigenprojections, total projection, analyticity      413
Eigenvalues      759
Eigenvalues, $\lambda$ -group of eigenvalues      400 413 420
Eigenvalues, algebraic, geometric multiplicity      104
Eigenvalues, algorithm for determining      506
Eigenvalues, analyticity      399 420 421
Eigenvalues, analyticity, single real parameter      422
Eigenvalues, behaviour near a critical point      401
Eigenvalues, continuity      399
Eigenvalues, continuity, single real parameter      399
Eigenvalues, differentiability      425 428
Eigenvalues, differentiability, single real parameter      399
Eigenvalues, n-tuple of eigenvalues      399
Eigenvalues, sensitivity      403
Eigenvectors      759
Eigenvectors, analyticity      415
Eigenvectors, differentiability      425 428
Eigenvectors, generalized      105
Eigenvectors, sensitivity      424 428
Electrical circuit      39—50 94 95 122
Energy, dissipation      31
Energy, kinetic      28 30
Energy, potential      28 31
Energy, thermal      70
Entire function      173 727
Equilibrium state      87 199 214
Ergodic set      211
Event space      77
Evolution operator      101 254 428
Fam — Meditch Theorem      387
Faraday's law      43
Feedback, dynamic output      161
Feedback, representation of model uncertainties      531 536 687
Feedback, static output      162
Feedback, static state      162
Feedback, well-posedness condition      164
Fejer's theorem      745
Fibonacci sequence      115
Finite escape time      84 85 199 230 690
Fisheries model      98
Flip-flop      62 80
Flow, differentiable      81
Flow, global      196 206
Flow, local      196
Flow, time-invariant      196
Focus, stable and unstable      111
Fourier coefficients      744
Fourier series      171 745—746
Fourier series, generalized      754
Fourier transform      172 746
Fourier transform, discrete      139 749
Fourier transform, inverse transform      174 747
Fourier — Plancherel transform      172 748
Fourier's law      71
Frechet differentiable      485 756
Frequency response      145
Front locus      674
Function element      380 733
Gain response      145
Generalized coordinates      30
Generator of a semigroup      120 757
Gershgorin set      407
Gershgorin type uncertainty      552 580 589
Gershgorin's theorem      398 407 552
Godunov matrix      547
Goodwin's model      9 293
Gram — Schmidt orthogonalization      498
Gronwall's lemma      86
Gronwall's Lemma, generalized      85
Growth rate at an equilibrium point      288 289
Growth rate of a semigroup      264 406 649
Hahn — Banach theorem      632 660 755
Hamilton's equations      33
Hamilton's principle      32
Hamiltonian      33 217 246
Hamiltonian matrix      605
Hamiltonian matrix of a system      605
Hankel form      320
Hankel matrix      320—330
Hankel matrix, Kronecker's Theorem      323
Hankel matrix, singular extension      326
Hardy spaces on $\mathds{C}^{+}_{\alpha}$ , $\mathds{D}^{+}_{\gamma}$       750 751
Hardy spaces on $\mathds{C}_{+}$ , $\mathds{D}_{+}$       147
Hausdorff metric      374 545 555
Heat conduction equation      115
Herglotz' theorem      354
Hermite form      313 314
Hermite generating function      314
Hermite matrix of a polynomial      314—317
Hermite — Biehler theorem      303 334 335
Hermite — Hurwitz theorem      328
Hermite's theorem      317

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