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

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Год издания: 2005

Количество страниц: 817

Добавлена в каталог: 16.02.2014

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Предметный указатель

Hermitian matrix      722
Hermitian matrix, inertia      314
Hermitian matrix, positive definite      276 317 723
Hermitian matrix, positive semi-definite      446 723
Hermitian matrix, signature      314 723
Hermitian matrix, spectral theorem      723
Hessenberg form      493
Hessenberg form, algorithm for reducing to      495
Hessenberg form, reduced      495
Hilbert space      116 753
Hille — Yosida theorem      672
Hoelder norm      455 554 718
Hoelder's inequality for functions      740
Hoelder's inequality for sequences      735
hold      168 170
Hold equivalent system      178
Hold, $k^{th}$ -order      170
Holomorphic function      376 727
Hooke's law      14
Householder reflection      493
Householder transformation      492—493
Householder vector      493
Hurwitz matrix of a complex polynomial      338
Hurwitz matrix of a real polynomial      338 340
Identity Theorem      376 420 728
Impulse response      126 128
Inertia of a complex matrix      295 719
Inertia of a Hermitian matrix      723
Inertia of an Hermitian matrix      314
Inertia, Sylvester's Law of Inertia      723
Initial growth rate      653 662 675 676
Initial growth rate of normal systems      656
Inners of a matrix      350
Input-output operator on $\mathds{N}$       124 148
Input-output operator on $\mathds{R}$       134 150 602
Input-output operator on $\mathds{R}_{+}$       131 148 603
Input-output operator on $\mathds{Z}$       150
Input-output system      135 see
Input-output system, $L^{q}$ -stable      132 137
Input-output system, linear      136
Input-output system, time-invariant      136
Input-state map      119 124
Input-to-state map      101
Interconnection of linear systems      154
Interconnection of uncertain systems      535
Interconnection, feedback connection      161
Interconnection, parallel connection      160
Interconnection, series connection      160
Interlacing condition on the real line      303
Interlacing condition on the unit circle      345
Interval polynomial      389 641
Invariant set      197 213 237 238
Invariant set, weakly      197 237
Inverted pendulum      22 35 110 176
Jenkin's governor      306
Joint Liapunov function      704 708
Joint Liapunov function, joint Liapunov norm      676
Jordan curve theorem      725
Julia set      210
Jury matrix      350
Jury's Stability Criterion      350
Kharitonov polynomials      390 641
Kharitonov's Theorem      391
Kirchhoff's laws      52
Kreiss — Spijker Theorem      670
Kronecker product      486 489 720
Kronecker symbol      143
Kronecker's theorem      323
Kronecker's Theorem, topological version      325
Lagrange's equations      31
Lagrangian      31
Laplace transform      139 742
Laplace transform, inverse      142 742
Laplace's equation      41
Laplacian      41 71
LaSalle's invariance principle for flows      227
LaSalle's invariance principle for time-invariant flows      238
Laurent series      320 730
Laurent — Puiseux series      419
Legendre transformation      33 38
Liapunov equation, algebraic      283 665
Liapunov equation, differential, difference      273 668
Liapunov equation, generalized      357 359
Liapunov exponent      258 259
Liapunov function for flows      222
Liapunov function for time-invariant systems      236
Liapunov function for time-varying systems      231
Liapunov function of maximal robustness      704
Liapunov function, joint      see "Joint Liapunov function"
Liapunov function, quadratic, for linear systems, time-invariant      282—290
Liapunov function, quadratic, for linear systems, time-varying      272—282
Liapunov operator      284 488
Liapunov operator, generalized      283 358
Liapunov transformation      262
Liapunov's direct method      217
Liapunov's direct method, instability theorems for flows      226
Liapunov's direct method, instability theorems, time-invariant linear      285
Liapunov's direct method, instability theorems, time-invariant nonlinear      245
Liapunov's direct method, instability theorems, time-varying linear      273 277
Liapunov's direct method, instability theorems, time-varying nonlinear      234
Liapunov's direct method, stability theorems for flows      223 227 248
Liapunov's direct method, stability theorems, time-invariant linear      285
Liapunov's direct method, stability theorems, time-invariant nonlinear      236
Liapunov's direct method, stability theorems, time-varying linear      273 276
Liapunov's direct method, stability theorems, time-varying nonlinear      232 233
Liapunov's indirect method      253
Liapunov's indirect method, exponential stability theorem      289
Liapunov's indirect method, instability theorem, time-invariant      288
Liapunov's indirect method, instability theorem, time-varying      281
Liapunov's indirect method, stability theorem, time-invariant      288 696
Liapunov's indirect method, stability theorem, time-varying      279
Lienard — Chipart Theorem      336 340
Lienard's equation      250
Limit cycle      203
Limit cycle, stable      204
Limit point      202
Limit set      202—204 208 209 214
Linear fractional transformation      538
Linear fractional transformation, sum, product, inverse      541
Linear operator, adjoint      662 757
Linear operator, bounded      124 756
Linear operator, closed      756 761
Linear operator, compact      756 761
Linear operator, normal      573 758 761
Linear operator, selfadjoint      758
Linear operator, unbounded      120 757
Linear system      100
Linear system, decomposition principle      100
Linear system, difference      103
Linear system, differentiable      101
Linear system, isomorphism      155
Linear system, morphism      155
Linear system, similar      35 156
Linear system, superposition principle      100
Linear system, time-invariant      102
Linear system, time-varying      101
Linearization      92
Linearization about a trajectory      280
Linearization about an equilibrium point      279 288
Lipschitz, continuous, locally Lipschitz      235 680 695
Lipschitz, gain      688 689
Lipschitz, global Lipschitz condition      688 695
Logarithmic norm      see "Initial growth rate"
Logistic growth model      3 98 215
Lorentz force      44
Lorenz attractor      212 241
Lotka — Volterra model      see "Predator-prey system"
Lumped parameter models      14
Markov parameter      125
Mass-spring system      13—17 94 157

Mathieu's equation      274
Maximum principle      588 592
Maximum principle for holomorphic functions      733
Maximum principle for subharmonic functions      734
Maximum principle, extended      734
Maxwell's equations      43
Meromorphic function      376 377 729
Minimal set      203 209
Minkowski functional      659 756
Model uncertainties      517 see
Moebius map      268 343 617
Moebius transform of a polynomial      343 387
Momentum, angular      18 19
Momentum, linear      17
Monodromy theorem      733
Morera's theorem      728
Multi-model      518
Multiplication operator on $i\mathds{R}$ , $\partial\mathds{D}$       149
Multiplication operator on $\mathds{C}_{+}$ , $\mathds{D}_{+}$       148
Neglected dynamics      690 697
Network, combinational switching      56
Network, electrical      50—55
Network, sequential switching      56 80
Newton's second and third laws      13
Non-wandering set      207 208
Norm of input-output operator      602
Norm, absolute      404 717
Norm, compatible      450 716
Norm, dual      455 466 715 755
Norm, Frobenius      456 718
Norm, Hoelder      455 554 717
Norm, Liapunov      663
Norm, Liapunov, $\beta$ -Liapunov      663 676
Norm, Liapunov, strict      663
Norm, monotone      717
Norm, operator norm      716
Norm, p-norm of a function      739
Norm, p-norm of a sequence      715
Norm, p-norm of a vector      735
Norm, rank one consistent      455 463 559 718
Norm, sub-multiplicative      404
Normality of a matrix family at a point      420—422
Numerical range      662
Numerical stability      268
Nyquist plot      145 593
Observable, uniform      276 285
Ohm's law      39
Open mapping theorem      528 755
Orbit      78
Orthonormal      423 753
Orthonormal, basis      117 432 754
Oscillations, parasitic      185 271
Oscillator, linear      16 108 129
Oscillator, multivariable      698 699
Oscillator, nonlinear      111 250 290 706
Oscillator, perturbed, spectral value sets      522 529 557
Oscillator, perturbed, stability radii      593 697
Ostrowski matrix      622
Parity check machine      58 95
Pendulum      25 82
Pendulum, stability analysis      241
Periodic points      214
Periodic system      262 266
Periodic system, criteria for stability      256
Perron's example      259
Perturbation norm      450 456 688
Perturbations of polynomials of one coefficient      627
Perturbations of polynomials, complex structured      628
Perturbations of polynomials, complex unstructured      633
Perturbations of polynomials, minimum norm complex      632
Perturbations of polynomials, minimum norm real      633 645
Perturbations of polynomials, real structured      637
Perturbations of polynomials, real unstructured      642
Perturbations of polynomials, scaled unstructured      630 640
Perturbations of polynomials, unstructured      626
Perturbations of systems, affine      530
Perturbations of systems, block-diagonal      456 536
Perturbations of systems, block-diagonal, diagonal      458
Perturbations of systems, block-diagonal, multi-block      457 550 588
Perturbations of systems, block-diagonal, specified block multiplicities      463
Perturbations of systems, complex structure      453
Perturbations of systems, full-block      454
Perturbations of systems, full-block, complex      556 591
Perturbations of systems, full-block, real      561 596
Perturbations of systems, full-block, unstructured      569 609
Perturbations of systems, linear fractional      537 544 586
Perturbations of systems, minimum norm      699
Perturbations of systems, minimum norm, complex      558 559 593
Perturbations of systems, minimum norm, real      563 565 568 597 601
Perturbations of systems, neglected dynamics      690 697
Perturbations of systems, nonparametric, dynamic      688
Perturbations of systems, nonparametric, linear time-varying      688 709
Perturbations of systems, nonparametric, nonlinear time-invariant      688
Perturbations of systems, nonparametric, nonlinear time-varying      689
Perturbations of systems, off-diagonal      552 580 589
Phase increasing property, Hurwitz      299
Phase increasing property, Hurwitz, real case      300
Phase increasing property, Schur      341
Phase portrait      82 111 243 652
Phase response      145
Plancherel's Theorem      172 748
Poincare — Bendixson theorem      203
Poincare's recurrence theorem      208
Poisson stability      208
Poisson's equation      41
Polar Plot      145 146
Pole      146 308 521 729
Polynomial      see also "Roots of a polynomial"
Polynomial with analytic coefficients      376
Polynomial, even and odd parts      302 639
Polynomial, Hermitian      357
Polynomial, Hurwitz      297 384
Polynomial, irreducible      377
Polynomial, leading coefficient      370
Polynomial, monic      370
Polynomial, positive pair      303
Polynomial, real and imaginary parts      311
Polynomial, recursive      322
Polynomial, reflection of Hurwitz polynomial      299
Polynomial, reflection of Schur polynomial      342
Polynomial, rotation of      342
Polynomial, Schur      340 384
Polynomial, symmetric, Hurwitz polynomial      299
Polynomial, symmetric, Schur polynomial      342
Positive definite, function      220
Positive definite, function, away from a closed set      219
Positive definite, matrix      see "Hermitian matrix"
Positive system      247 601
Predator-prey system      4—6 243 518
Proper rational function, strictly      141 320
Pseudospectra      531 569 669
Pseudospectra, characterization      569
Pseudospectra, characterization for complex normal matrices      573
Pseudospectra, characterization for real normal matrices      576
Pseudospectra, lower bounds, complex case      573
Pseudospectra, lower bounds, real case      576
Pseudospectra, under similarity transformations      579 583
Puiseux series      382 401 528
Pulse amplitude modulation      169
QR algorithm      502
QR factorization      497
Quotient system      157
Rational dependence on parameters      521 539
Rational systems in the plane      209
Real perturbation values, lower      483
Real perturbation values, upper      483
Real representation of complex matrices      465 600 720
Realness locus      562 568 597 600 638
Recurrence      206
Recurrent point      209

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