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

Rellich's theorem      420
Residue theorem      411 730
Resolvent operator      409 661 759
Resolvent operator, compact      761
Resolvent set      409 759
Resolvent, equation      409 759
Resolvent, partial fraction decomposition      410
Resultant      315 377
Riccati equation, algebraic      604 679 703
Riccati equation, algebraic, stabilizing solution      604
Riccati equation, differential      678
Riemann's lemma      138 745 747
Root locus      562 582
Root set of an uncertain polynomial      626
Root set of an uncertain polynomial, complex perturbations, scalar      636
Root set of an uncertain polynomial, complex perturbations, structured      628
Root set of an uncertain polynomial, complex perturbations, unstructured      633
Root set of an uncertain polynomial, real perturbations, interval polynomial      642
Root set of an uncertain polynomial, real perturbations, scalar      638
Root set of an uncertain polynomial, real perturbations, structured      628 638
Roots of a polynomial      370
Roots of a polynomial, analyticity      370 376
Roots of a polynomial, continuity      370 374
Roots of a polynomial, n-tuple of roots      373 374
Roots of a polynomial, sensitivity      370 383 636
Rouche's theorem      371 731
Routh array      305
Routh test      305
Saddle point      111
sample rate      169 192
Sampled system      175
Sampler      168
Sampling period      169
Sampling theorem      173
Samuelson — Hicks multiplier-accelerator      10
Scaling parameter      468 551
Scaling transformation      457 458 551 554 588
Schaefer's model      3
Schmidt pair      436
Schmidt — Mirsky theorem      436
Schur complement formula      606 719
Schur form of a matrix      499—501
Schur form of a matrix, algorithm for reducing to      502
Schur form of a matrix, complex      501
Schur form of a matrix, real      499
Schur generating function      347
Schur matrix of a polynomial      347
Schur test      355
Schur — Biehler Theorem      345
Schur — Cohn Theorem      349
Semi-norm      655 755
Semi-scalar product      660
Semi-simple      410
Semicontinuous, lower      465 724
Semicontinuous, upper      464 466 724
Semigroup      101 119
Semigroup, contraction      658 661
Semigroup, contraction, $\beta$ -contraction      658 663
Semigroup, contraction, strict      658 661 663
Semigroup, contraction, strong      658
Semigroup, generator      120 757
Semigroup, strongly continuous      120 672 756 761
Shift operator      89 132 137
Shift operator for functions      743
Shift operator for sequences      736 760
Singular value decomposition      435
Singular value decomposition of Kronecker product      722
Singular value decomposition, pseudo      439
Singular value decomposition, pseudo, analyticity      442
Singular value loci      609
Singular values      431
Singular values, algorithm for determining      508
Singular values, continuity      439
Singular values, pseudo      439
Singular vectors      432 436
Singular vectors, pair      436
Singularity of a complex function, isolated, removable, essential      729
Spectral abscissa      263 649
Spectral abscissa, $\delta$ -spectral abscissa      673
Spectral contour, complex perturbations      557
Spectral contour, real perturbations      563
Spectral Decomposition Lemma      105
Spectral mapping theorem      719
Spectral radius      453 760
Spectral radius, $\delta$ -spectral radius      684
Spectral representation      105 410 418
Spectral representation, analyticity      414 420 421
Spectral representation, analyticity, single real parameter      422
Spectral value set      522 545
Spectral value set of a direct sum of systems      546
Spectral value set, bounds      551
Spectral value set, characterization      550 551
Spectral value set, connected components      545 558—559 563—564
Spectral value set, continuity      555
Spectral value set, full-block complex perturbations      524 673
Spectral value set, full-block complex perturbations, boundary of      558
Spectral value set, full-block complex perturbations, characterization      556
Spectral value set, full-block real perturbations      524 561
Spectral value set, full-block real perturbations, boundary of      563
Spectral value set, full-block real perturbations, chacterization for l=1      564
Spectral value set, full-block real perturbations, chacterization for spectral norm      567
Spectral value set, full-block real perturbations, general characterization      562
Spectral value set, off-diagonal perturbations      554 580
Spectral value set, under similarity transformations      546
Spectral value set, unstructured      see "Pseudospectra"
Spectrum      759
Spectrum, point, residual, continuous      759
Spijker's Lemma      671 731
Splitting of an eigenvalue      400 401 573
Stability criteria for polynomials, Hurwitz polynomials, Bezout matrix      319 320
Stability criteria for polynomials, Hurwitz polynomials, Cauchy index      311
Stability criteria for polynomials, Hurwitz polynomials, change of argument, complex polynomial      298
Stability criteria for polynomials, Hurwitz polynomials, change of argument, real polynomial      300
Stability criteria for polynomials, Hurwitz polynomials, Hankel matrix      334
Stability criteria for polynomials, Hurwitz polynomials, Hermite matrix      317
Stability criteria for polynomials, Hurwitz polynomials, Hurwitz matrix, complex case      337
Stability criteria for polynomials, Hurwitz polynomials, Hurwitz matrix, real case      339
Stability criteria for polynomials, Hurwitz polynomials, Lienard — Chipart Theorem      336
Stability criteria for polynomials, Hurwitz polynomials, recursive test, real polynomial      305
Stability criteria for polynomials, Hurwitz polynomials, Routh test      305

Stability criteria for polynomials, Schur polynomials, change of argument      340
Stability criteria for polynomials, Schur polynomials, recursive test      355
Stability criteria for polynomials, Schur polynomials, Schur matrix      349
Stability criteria for polynomials, Schur polynomials, Schur — Biehler Theorem      345
Stability criteria for polynomials, Schur polynomials, Schur — Cohn Theorem      349
Stability criteria for polynomials, Schur polynomials, Toeplitz matrix      353
Stability criteria for systems      see also "Liapunov's indirect method" "Liapunov's
Stability criteria for systems, time-invariant linear systems via algebraic Liapunov equations      285
Stability criteria for systems, time-invariant linear systems, algebraic stability domains      357 359
Stability criteria for systems, time-invariant linear systems, spectral criteria      264
Stability criteria for systems, time-varying linear systems      260
Stability criteria for systems, time-varying linear systems via differential Liapunov equations      273 276
Stability definitions, $L^{q}$ -stability      132
Stability definitions, $\mathds{C}_{g}$ -stability      522
Stability definitions, (M, $\beta$ )-stability      648 664
Stability definitions, (M, $\beta$ )-stability of differential inclusions      677
Stability definitions, (M, $\beta$ )-stability, strict      648
Stability definitions, absolute stability      701
Stability definitions, asymptotic stability of a trajectory      199
Stability definitions, asymptotic stability of an equilibrium point      200
Stability definitions, exponential stability      707
Stability definitions, exponential stability for linear systems      257
Stability definitions, exponential stability of nonlinear systems      233
Stability definitions, global asymptotic stability      695
Stability definitions, global asymptotic stability of nonlinear systems      200 238
Stability definitions, global exponential stability      709
Stability definitions, marginal stability      218
Stability definitions, stability of a trajectory      199
Stability definitions, stability of an attractor      211
Stability definitions, stability of an equilibrium point      200
Stability definitions, uniform asymptotic stability of a trajectory      199
Stability definitions, uniform stability of a trajectory      199
Stability radius of polynomials      630
Stability radius of polynomials, complex perturbations of one coefficient      636
Stability radius of polynomials, complex perturbations, scalar      636
Stability radius of polynomials, complex perturbations, structured      630
Stability radius of polynomials, complex perturbations, unstructured      634
Stability radius of polynomials, real perturbations of one coefficient      640 644
Stability radius of polynomials, real perturbations, scalar      638
Stability radius of polynomials, real perturbations, scaled unstructured      640
Stability radius of polynomials, real perturbations, structured      630 638
Stability radius of polynomials, real perturbations, unstructured      642 645
Stability radius of systems      529 586
Stability radius of systems of a direct sum of systems      594 596
Stability radius of systems, (M, $\beta$ )-stability radius      675 678
Stability radius of systems, (M, $\beta$ )-stability radius, time-varying perturbations      677
Stability radius of systems, bound for multi-block perturbations      589
Stability radius of systems, characterization      587
Stability radius of systems, continuity, complex perturbations      615
Stability radius of systems, continuity, lower semicontinuity      614
Stability radius of systems, continuity, real perturbations      616 623
Stability radius of systems, full-block complex perturbations      591
Stability radius of systems, full-block complex perturbations, algorithm for computing      607
Stability radius of systems, full-block complex perturbations, characterization      591
Stability radius of systems, full-block complex perturbations, characterization for spectral norm      602—606
Stability radius of systems, full-block complex perturbations, continuous time      592
Stability radius of systems, full-block complex perturbations, discrete time      592
Stability radius of systems, full-block real perturbations      596
Stability radius of systems, full-block real perturbations, characterization for l=1      597
Stability radius of systems, full-block real perturbations, general characterization      600
Stability radius of systems, off-diagonal perturbations, continuous time      589
Stability radius of systems, off-diagonal perturbations, discrete time      591
Stability radius of systems, under dynamic perturbations      696
Stability radius of systems, under dynamic perturbations, real case      699
Stability radius of systems, under nonlinear perturbations      697
Stability radius of systems, under time-varying perturbations      697
Stability radius of systems, under unstructured perturbations      see "Distance from instability"
Stability region      265 522 529 585
Stability region, algebraic      357
Starlike set      521 707
State      see "Dynamical system"
State of a delay system      91
State of a shift register      80
State transition map      76
Steady state response      144
Step response      126
Strongly destabilizing perturbation      616
Structured singular value      450
Subharmonic function      592 733
Sublevel set      220 237
Sublevel set, attractive      240
Subsystem      156
Summability      140 753
Summability, absolute      753
Supply and demand curves      8
Sylvester's law of inertia      314 723
System embedding      156
System graph      165
System projection      157
Toeplitz matrix      352—354
Transfer function      140—142 549 587
Transfer function of feedback interconnection      162
Transfer function of parallel interconnection      161
Transfer function of series interconnection      160
Transfer function, dyadic decomposition      143
Transfer function, experimental identification      144
Transfer matrix      see "Transfer function"
Transient amplification factor      650
Transient behaviour      648
Transient behaviour, ideal      656
Transient bound of a linear system      650 669 671
Transient bound of a linear system, normal system matrix      656 672
Transient bound, structured      672 673
Transient bound, time-varying nonlinear perturbations      679 680
TREE      51
Tree, spanning      51
Trolley example      15
Unimodal      474
Unit impulse      125
Value set      390
van der Pol equation      244
Verhulst model      see "Logistic growth model"
Volume preserving flow      207
Wandering point      206
Well-posedness radius      521 538 544 556 561 587 629
Weyl's theorem      445
Wilkinson polynomial      384 636
Wilkinson shift      509
Winding number      310 725 727
z-transform      139 737

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