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Antsaklis P.S., Michel A.N. — Linear Systems
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Название: Linear SystemsАвторы: 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
Язык: Рубрика: Технология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 670Добавлена в каталог: 28.03.2010Операции: Положить на полку |
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Output, reachability, controllability 312 Output, vector 4 Output, zeroing, or blocking, property 307 Parallelogram law 438 Parseval's identity 440 Partial state 519 Partial sum 21 Partially ordered set 27 Peano — Baker series 56 143 147 Pendulum, inverted 89 380 Pendulum, simple 16 52 82 93 Pendulum, two-link 83 Periodic solution 492 see Periodic system 11 62 161 Phase, plane 198 Phase, portrait 88 Phase, variable 198 Picard iteration 31 Piecewise continuous 58 Piecewise continuous, derivative 23 Piecewise continuous, function 9 Plant 182 Pole assignment problem 330 658 see Pole polynomial 299 Poles at infinity 319 Poles of a transfer function 298 299 301 488 508 563 Poles of the system 298 301 564 see Polynomial matrices 524 Polynomial matrices, column, row reduced 526 Polynomial matrices, common divisors 535 Polynomial matrices, coprime, left, right 536 612 Polynomial matrices, division theorem 545 Polynomial matrices, doubly coprime 593 Polynomial matrices, equations 540 653 Polynomial matrices, equivalent 535 Polynomial matrices, Hermite form 532 Polynomial matrices, proper or reduced row, column 527 Polynomial matrices, rank 524 Polynomial matrices, regular 528 Polynomial matrices, Smith form 298 531 Polynomial matrices, unimodular 526 Polynomial matrix description 517 519 521 553 see Polynomial matrix interpolation 653 Polynomial of linear transformation 104 Polynomial vector, degree 526 Polynomial vector, linear independence 524 Polynomial, Hurwitz 462 Polynomial, monic 132 298 Polynomial, stable 462 Positive definite 437 443 469 491 see "Matrix" Positive indefinite 469 see "Matrix" Positive innerwise 498 Positive orbit 492 Positive semidefinite 437 443 469 470 491 see "Matrix" Positively invariant 492 Prediction estimator 360 Proper rational matrix 391 Proper transfer function 170 Proper value 102 see Proper vector 122 see Pythagorean Theorem 439 QR decomposition 647 Quadratic form 436 Quantization 183 Radially unbounded 491 see Range space 100 Rank 107 524 Rank of a functional 437 Rank, normal 306 525 Rank, test 274 Rational function, biproper 552 577 Rational function, proper and stable 552 Rational matrix, equations 653 Rational matrix, right inverse 313 Rational matrix, Smith — McMillan form 299 563 Rayleigh's dissipation function 83 Reachability 214 215 226 235 242 244 see from Reachability, continuous-time system 227 235 see from Reachability, discrete-time system 215 241 see from Reachability, Gramian 230 236 245 see from Reachability, matrix see "Controllability" see from Reachability, output 312 see from Reachability, subspace 228 235 242 see from Reachable 217 228 235 see "Controllability from Reachable pairs 228 see "Controllability from Reachable state 242 see "Controllability from Reachable subspace 217 228 235 242 see "Controllability from Real numbers 8 Real sequence 17 Real vector space 38 Realization algorithms 402 Realization algorithms, block companion form 418 Realization algorithms, controller/observer form 404 Realization algorithms, matrix A diagonal 417 Realization algorithms, singular value decomposition 423 Realization of systems 383 385 388 565 Realization of systems, existence and minimality 390 394 565 Realization of systems, impulse response 386 Realization of systems, least order, irreducible, minimal order 394 401 565 Realization of systems, order of 394 Realization of systems, pulse response 388 Realization of systems, transfer function 202 388 389 Reconstructible 255 see Reduced order model 424 Reference input 326 Relation 535 Response 4 59 61 Response, maps 625 Response, total 165 166 174 176 Response, zero-input 146 165 177 Response, zero-state 146 165 166 177 Resultant 542 Return difference matrix 586 Riccati equation 343 349 358 363 Riccati equation, continuous-time case 342 343 358 Riccati equation, discrete-time case 349 363 Ring 552 Ring, euclidean 551 RLC circuit 14 16 206 276 Robust control 327 Rosenbrock system equivalence 555 Rosenbrock system matrix 301 554 564 Routh — Hurwitz stability criterion 466 Row 107 see Row reduced 526 see Row, Hermite form 532 see Row, proper see "Polynomial matrices" see Row, rank 119 see Row, vector 107 see Sampled data system 65 182 183 319 Sampling period, rate 185 scalar 38 Schur — Cohn stability criterion 498 Schwarz inequality 42 49 438 Semi-group property 175 Sensitivity matrix 599 626 Separation principle, property 325 365 SEQUENCE 17 Sequence, functions 18 Sequence, vectors 44 Series 203 Shift operator 68 92 Signal, digital 183 Similarity transformation 116 120 151 singular 101 see "Matrix" Singular, value 648 see "Matrix" Singular, value decomposition 423 430 648 650 see "Matrix" Singular, vector, left, right 651 see "Matrix" Skew adjoint 443 Skew symmetric 435 436 Smith form 298 531 533 see Smith — McMillan form 298 299 563 see Solutions of algebraic equations 101 115 646 655 657 see Solutions of difference equations, particular 64 see Solutions of difference equations, total 64 see Solutions of differential equations 10 12 see Solutions of differential equations, 23 see Solutions of differential equations, bounded 452 see Solutions of differential equations, continuable 27 see Solutions of differential equations, continuation 26 27 28 31 37 45 54 see Solutions of differential equations, continuous dependence 33 37 45 see Solutions of differential equations, continuous dependence on initial conditions 45 54 see Solutions of differential equations, continuous dependence on parameters 47 54 see Solutions of differential equations, Euler's method 25 85 see Solutions of differential equations, existence 25 37 45 54 see Solutions of differential equations, homogeneous 58 64 145 see Solutions of differential equations, noncontinuable 27 see Solutions of differential equations, particular 58 64 145 see Solutions of differential equations, Peano — Baker series 56 143 147 see Solutions of differential equations, periodic 492 see Solutions of differential equations, predictor-corrector method 86 see Solutions of differential equations, Runge — Kutta 85 see Solutions of differential equations, successive approximations 31 47 143 see Solutions of differential equations, total 58 see Solutions of differential equations, uniqueness 29 30 32 45 see Solutions, bounded 491 493 see Space of linear transformations 102 Space of n-tuples 38 Space of real-valued continuous functions 39 Space, span 97 Spectral theorem 445 Spectrum 122 Spring 16 88 320 Spring mass system 13 82 83 206 320 Stability 445 492 560 see Stability, algebraic criteria 461 462 see Stability, asymptotic 159 189 449 491 494 497 504 563 see Stability, asymptotic in the large 450 491 494 499 see Stability, attractive equilibrium 449 see Stability, bounded-input/bounded-output (BIBO) 481 490 505 see Stability, causal 67 70 71 77 see Stability, domain of attraction 449 491 see Stability, exponential 449 477 480 512 see Stability, exponential in the large 450 459 471 see Stability, external 481 490 506 see Stability, gap and position criterion 464 see Stability, global asymptotic 491 492 494 499 see Stability, graphical, geometric criteria 462 see Stability, input-output 452 481 490 505 see Stability, interlacing 464 see Stability, internal 452 481 490 613 623 see Stability, Leonhard — Mikhailov criterion 463 see Stability, linear systems, continuous 159 see Stability, linear systems, discrete 189 see Stability, Lyapunov 445 448 590 see Stability, Routh — Hurwitz criterion 466 see Stability, Schur — Cohn 498 see Stability, uniform 448 see Stability, uniform asymptotic 449 see Stability, uniform asymptotic in the large 450 459 461 see Stabilizable 330 Stable 159 189 448 452 455 459 491 492 see Standard form, Kalman's canonical 269 Standard form, uncontrollable system 264 265 Standard form, unobservable system 267 268 State 56 58 60 228 235 State constructibility 251 260 see State controllability 229 235 242 see State equation 5 58 61 165 State equation, linear solution 55 145 State estimator 351 359 see State feedback 321 322 326 605 see State feedback, input-output relations 345 see State observability 250 258 see State observer 321 322 350 359 608 State observer, current 360 State observer, full-order 350 358 State observer, identity 350 359 State observer, optimal 357 362 State observer, partial state 354 362 608 State observer, reduced-order 355 362 State reachability 215 235 242 243 see State space 56 58 State space description 5 see State space description, continuous-time 58 see State space description, discrete-time 60 see State transition matrix 56 63 143 State unconstructible 250 255 State unobservable 248 253 258 State, controllable 242 State, partial 519 State, phase variable 198 State, variables 4 56 58 61 State, vector 4 56 58 Static decoupling 634 Static output feedback 379 Structure theorem, controllable version 291 Structure theorem, observable version 297 Subsequence 18 Successive approximations 31 47 see Superposition principle 60 66 Sylvester matrix 541 Sylvester rank inequality 205 396 Sylvester resultant 542 Sylvester theorem 437 symmetric 435 436 648 see System at rest 71 77 System interconnections, feedback 203 573 System interconnections, parallel 203 568 System interconnections, series, or tandem 203 570 System representations, balanced 430 System representations, differential/difference operator 517 System representations, equivalence, of 170 180 554 System representations, external 65 System representations, fractional, left, right 517 521 System representations, input normal 430 System representations, input-output 66 System representations, integral 72 75 76 System representations, internal 5 619 System representations, linear continuous-time 76 System representations, linear discrete-time 68 System representations, matrix fractional 521 612 619 System representations, output normal 430 System representations, polynomial matrix 517 519 521 553 System representations, standard form, uncontrollable, unobservable 265 267 268 System representations, state space 5 System representations, zero-input equivalence 170 171 173 181 System representations, zero-state equivalent 170 171 173 181 System with memory 67 System, autonomous 12 62 System, classification 3 System, composite 203 System, conservative 81 System, continuous time 4 System, description, external 5 65 System, discrete-time 5 60 68 174 System, distributed parameter 3 System, dual 222 402 System, finite dimensional 3 4 5 System, Fuhrmann equivalence 554 System, Hamiltonian 81 System, hybrid 3 183 System, infinite dimensional 3 System, input 66 System, inverse 377 634 System, linear 60 66 94 509 System, linear time-invariant 59 61 System, linear time-varying 59 61 System, lumped parameter 3 System, matrix 301 564
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