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Antsaklis P.S., Michel A.N. — Linear Systems
Antsaklis P.S., Michel A.N. — Linear Systems



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Название: Linear Systems

Авторы: Antsaklis P.S., Michel A.N.

Аннотация:

"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook! …The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years. The result is a comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control." —IEEE Transactions on Automatic Control

"In assessing the present book as a potential textbook for our first graduate linear systems course, I find...[that] Antsaklis and Michel have contributed an expertly written and high quality textbook to the field and are to be congratulated…. Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference." —Automatica

Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook.

The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control.

Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The book’s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 670

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-approximate solution      23
Abel's formula      140
Ackermann's formula      334 353
Adjoint equation      197
Adjoint of a matrix      115 442
Aircraft      209 320 381
Algebra      102
Algebra, associative      103
Algebra, commutative      103
Algebraic equation      115 see
Algebraic multiplicity      124 444 see
Algebraic Riccati equation      343 349 358 363 see
Algebraically closed      123 see
Ascoli — Arzela lemma      22
Asymptotic behavior      156 186 see
Asymptotic state estimator      351 see
Asymptotically stable      159 189 449 491 494 497 504 563 see
Asymptotically stable in the large      450 491 494 499 see "Globally
At rest      71 77 see
Attractive      449 491 see
Automobile suspension system      207 380
Autonomous      11 62 see "System"
Axioms of a field      37
Axioms of a metric      438
Axioms of a norm      438
Axioms of a vector space      38
B-W property      18 see
Balanced representations      430
Basis      99 100 170 439 551 552 see
Bessel's inequality      440
Bezout identity      553 612 see
BIBO stable      481 490 505 see
Bijective      101 102 see
Bilinear functional      435
Bilinear functional, signature      435
Bilinear functional, symmetric      435 436
Binet — Cauchy formula      639
Biproper      552 577 see
Block diagonal      130 see
Blocking property      307 see
Bolzano — Weierstrass property      18 44
Bounded      491 493 see
Bounded-input/bounded-output stability      481 482 483 484 490 505 see
Brunovsky canonical form      288 see
Building, earthquake protection      208
Canonical form      116 127 535
Canonical form, Brunovsky      288
Canonical form, Jordan      130 135 136
Canonical Structure Theorem      270 see
Cartesian product      8
Cauchy criterion      20
Cauchy sequence      18
Cauchy — Peano existence theorem      25
Causal      67 70 71 77 see
Cayley — Hamilton theorem      124 154
Characteristic equation      123
Characteristic exponent      163
Characteristic polynomial      123 299 563 see "Transfer
Characteristic value      122 see
Characteristic vector      122 see
Chemical reaction process      381
Cholesky decomposition      647
Closed loop control      327
Cofactor      113 see
Column rank      119 see
Column reduced      526 see
Column vector      107 see
Command input      326 see "Reference
Common divisor      535
Common divisor, left      536
Common divisor, right      536 see
Commutative algebra      103 see
Compact set      9 18
Companion form      131 153 468 see
Complete instability      473 501 see unstable"
Complete space      18
Completeness property      288
Complex vector space      38
Composite system      203 see
Condition number      646 647 649 see
Conformal matrices      109 see
Congruent matrices      435 436 see
Conservative system      81 see
Constructibility      219 247 251 252 260
Constructibility, continuous-time system      248 252
Constructibility, discrete-time system      219 257
Constructibility, Gramian      251 256 262 see
Continuation of solutions      26 27 31 37 see
Continuous dependence of solutions      37 see
Continuous function at a point      9 44
Continuous function over an interval      9
Continuous function, uniformly      9
Continuous time systems      4 see
Control problems      632
Controllability      214 215 228 235 242 264 265 274 561
Controllability from the origin      215 217 228 236 see
Controllability to the origin      215 218 228
Controllability, continuous-time system      227 235
Controllability, discrete-time system      215 241
Controllability, eigenvalue/eigenvector (PBH) test      272
Controllability, Gramian      233 240 245
Controllability, index      283
Controllability, matrix      217
Controllability, output      312
Controllability, subspace      229 236 242
Controllable      228 235 561
Controllable companion form      279
Controllable eigenvalues      265
Controllable mode      265
Controllable pair      229
Controllable single-input      373
Controllable state      242
Controllable subspace      229 236 242
Controllable, differentially      315
Controllable, instantaneously      315
Controllable, uniformly      315
Controller companion form      203
Controller form      279 280 285 291
Controller form, multi-input      283
Controller form, single-input      280
Controller with two degrees of freedom      368 622
Controller, digital      182
Controller, feedback      589
Controller, implementations      629
Convergence of a function      18
Convergence of a function, pointwise      18 19 44
Convergence of a function, uniform      18 19 20
Convergence of a sequence      18 44
Convergence of a series      21
Convergence of a series, pointwise      21
Convergence of a series, uniform      21
Converse theorem      513
Converter (A/D, D/A)      183
Convolution, integral      78
Convolution, sum      70
Coordinate representation      100 see
Coprime      535 593 see "Polynomials"
Critical      460 462 see
Cyclic      132 see
D/A converter      183
Dead-beat, control      201
Dead-beat, observer      359
Decoupling indices      377 see
Decoupling, diagonal      377 378 633
Decoupling, static      634
Degree, McMillan      397
Degree, McMillan, polynomial vector      526
Detectable      351
Determinant      112 121 586 see "Matrix" "Return
Determinantal divisor      299 534
Diagonal decoupling      377 378 633
Difference equations      62 63 see
Differential equations, ordinary, classification      11 see
Differential equations, ordinary, first-order      10 see
Differential equations, ordinary, linear      47 see
Differential equations, ordinary, linear homogeneous      13 138 see
Differential equations, ordinary, linear homogeneous with constant coefficients      148 see
Differential equations, ordinary, linear nonhomogeneous      138 145 see
Differential equations, ordinary, nth order      12 see
Differential equations, ordinary, systems of first order      37 see
Digital controller      182
Digital filter      65
Digital to analog converter      183
DIMENSION      99 see
Diophantine equation      540 612 656
Diophantine equation, all solutions      550
Diophantine equation, Bezout identity      553 612
Diophantine equation, historical remarks      552
Dirac delta distribution      72 74 154
Direct form      65
Direct link matrix      169
Direct sum      126
Discrete-time impulse      68 178
Discrete-time Kalman filter      363 see
Discrete-time system      3 5 60 66 174 215 241 242 257 348 358 362 388 392 401 489 see
Distance function      438
Divisor, common      535
Divisor, greatest common      535 536
Divisor, left, right      536
Domain of attraction      449 491 see
Double integrator      205
Doubly coprime      593 see
Dual system      222 402
Economic model      205 382
Eigenvalue      121 122 298 301 305 564
Eigenvalue or pole assignment      328 330 658
Eigenvalue or pole assignment, direct method      328
Eigenvalue or pole assignment, eigenvector assignment      337
Eigenvalue or pole assignment, using controller form      332
Eigenvalue, algebraic multiplicity      124 444
Eigenvalue, controllable      265
Eigenvalue, critical      460 462
Eigenvalue, geometric multiplicity      122
Eigenvalue, repeated      129
Eigenvalue, spectrum      122
Eigenvector      121 122
Elementary operations, column      526
Elementary operations, row      526
Elementary unimodular matrices      526
Eliminant matrix      542 547
Equicontinuous      22 46
Equilibrium      158 189 445 446 490 see
Equilibrium, asymptotically stable      158 189 449 491 494 497 504 563 see
Equilibrium, asymptotically stable in the large      450 491 494 499 see
Equilibrium, attractive      449 491 see
Equilibrium, completely unstable      473 501 see
Equilibrium, domain of attraction      449 491 see
Equilibrium, exponentially stable      449 480 512 see
Equilibrium, exponentially stable in the large      450 459 471 see
Equilibrium, globally asymptotically stable      450 491 494 499 see
Equilibrium, isolated      446 see
Equilibrium, qualitative characterization      447 see
Equilibrium, stable      159 189 448 452 455 459 491 492 see
Equilibrium, trivial solution      138 446 see
Equilibrium, uniformly asymptotically stable      449 see
Equilibrium, uniformly asymptotically stable in the large      450 459 451 see
Equilibrium, uniformly stable      448 453 454 455 459 461 470 512 see
Equilibrium, unstable      159 189 450 459 462 472 479 481 491 495 497 499 504 513 see
Equivalence of internal representations      170 180 554
Equivalence, relation      535
Equivalence, transformation      181
Equivalent      116 119 172 181 535 554
Estimator      361 see
Euclidean norm      42
Euclidean ring      551
Euclidean space      437 441
Euler method      25 65 85
Euler polygon      25
Exponentially stable      449 477 480 512 see
Exponentially stable in the large      450 459 471 see
Extended system matrix      557
External input      326
External system description      5 65 see
Feedback      326 589
feedback control systems      58 589 590 see "Output
Feedback stabilizing controller      589
Feedback stabilizing controller, paramererizations      592
Feedback stabilizing controller, parameterizations, proper and stable (MFD)      611 615
Feedback stabilizing controller, two degrees of freedom      622
Feedback, configuration      203 573
Feedback, gain matrix      327
Feedback, integral      379
Feedback, output      363 379 658
Feedback, state      321 323 324 326 327 364 658
Fermat's last theorem      553
Field      37
Field, algebraically closed      123
Field, complex numbers      38
Field, rational functions      37
Field, real numbers      38
Filtering theory      357
Floquet multipliers      163
Force field, inverse square law      52
Fractional description      521 see
Frequency response      204 463 465
Frobenius norm      653
Function      8
Function, bijective      101
Function, continuous      9
Function, Hamiltonian      81
Function, indefinite      437 469
Function, negative definite, semidefinite      437 491
Function, one-to-one, orinjective      101
Function, onto, or surjective      101
Function, piecewise continuous      9 58
Function, positive definite, semidefinite      437 469 491
Fundamental matrix      139 140
Fundamental sequence      18
Fundamental set of solutions      140
Fundamental theorem of linear equations      101
Gap and position criterion      465 see
Gaussian elimination      647
Generalized distance function      468 see
Generalized energy function      468 see
Generalized function      74 see
Geometric multiplicity      122 see
Globally asymptotically stable      491 494 see "Equilibrium"
Gram — Schmidt process      440
Gram, determinant      234
Gram, matrix      234
Gramian constructibility      251 256 262
Gramian controllability      233 240 246
Gramian observability      249 253 259
Gramian reachability      230 236 245
Graphical criteria      462 see
Gronwall inequality      29
H-B property      18 44
Hamiltonian dynamical system      81
Hamiltonian function      81
Hamiltonian matrix      344 349
Hankel matrix      399
Hard disk, read/write head      212 382
harmonic oscillator      198
Heine — Borel property      18 44
Hermite form      532
Hermitian matrix      648
Highest degree coefficient matrix      526
homogeneous differential equations      138 see
homogeneous solution      58 64 145 see
Hurwitz matrix      460
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