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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.
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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
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Предметный указатель
-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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