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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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Hurwitz polynomial 462 Hybrid system 3 183 Idempotent matrix 126 Identity matrix 110 Identity transformation 103 Ill-conditioned 647 Impulse response matrix 71 77 78 79 165 166 177 Impulse response, continuous-time 75 77 Impulse response, discrete-time 70 Impulse response, time-invariant 78 Impulse response, time-varying 79 Index, bilinear functional 437 Index, nilpotent operator 134 Index, set 17 Indices, controllability 283 Indices, decoupling 377 Indices, Kronecker 288 Indices, observability 295 Induced norm 43 Infinite series method 150 see exponential" Infinite series, convergence 21 Initial conditions 4 5 Initial time 4 5 61 62 Initial value problem 10 11 12 62 Initial value problem, examples 13 Initial value problem, existence of solutions 21 Inner product 437 Inners 498 Input, command, or reference 326 Input, comparison sensitivity matrix 626 Input, decoupling zeros 302 564 Input, external 326 Input, function observability 302 Input, normal representations 430 Input, output decoupling zeros 302 564 Input, output stability 451 481 Input, vector 4 Input-output description 5 65 165 174 see Input-output stability 481 505 see Instability 159 189 450 459 472 479 481 491 495 497 499 504 513 see unstable" Integral equation 11 Integral feedback 379 Integral representation 72 75 76 Integration, forward rectangular rule 85 Interconnected systems 568 Interconnected systems, feedback 573 Interconnected systems, parallel 568 Interconnected systems, series 570 Interlacing 464 see Internal description 5 see Internal qualitative properties 490 see Internal stability 448 451 481 490 623 624 Internally balanced realization 424 430 see Interpolation of polynomial, rational matrix 653 Invariance principle 493 see Invariant factors, polynomials 298 534 Invariant property of (A, B) 288 Invariant subspace 260 Invariant zeros 302 306 563 564 565 see Inverse system 377 634 Inverse z-transformation 178 Inverted pendulum 89 380 see Jacobian matrix 48 447 Jordan canonical form 130 135 136 Kalman filter, continuous-time 352 Kalman filter, discrete-time 363 Kalman — Bucy filter 357 Kalman's Decomposition Theorem 269 270 Kronecker indices 288 La Salle's Theorem 493 see "Invariance Lagrange's equation 83 Lagrangian 83 Lamda approach 622 Laplace transform 75 154 Latent value 122 see Least squares 648 652 Least-order realization 394 Left coprime 536 see Leonhard — Mikhailov stability criterion 463 Level curve 471 see Lienard equation 16 479 Limit cycle 88 Linear algebraic equation, fundamental theorem 101 Linear algebraic equation, homogeneous, nonhomogeneous 115 646 Linear manifold 97 Linear matrix pencil 288 640 Linear operator 40 see Linear operator, nilpotent 134 see Linear ordinary difference equation, autonomous 12 Linear ordinary difference equation, homogenous 62 63 174 Linear ordinary difference equation, homogenous w/constant coefficients 175 Linear ordinary difference equation, matrix 140 495 Linear ordinary difference equation, nonhomogenous 62 63 Linear ordinary difference equation, periodic 12 13 62 63 161 Linear ordinary differential equation, autonomous 12 see Linear ordinary differential equation, homogeneous 12 13 62 63 138 174 see Linear ordinary differential equation, homogeneous w/constant coefficients 148 164 175 see Linear ordinary differential equation, matrix 140 495 see Linear ordinary differential equation, nonhomogeneous 12 54 62 63 145 see Linear ordinary differential equation, periodic 12 13 62 63 161 see Linear ordinary differential equation, systems, continuation 54 see Linear ordinary differential equation, systems, continuity with respect to parameters 54 see Linear ordinary differential equation, systems, existence 54 see Linear ordinary differential equation, systems, uniqueness 54 see Linear space 37 see Linear subspace 97 126 Linear subspace, direct sum 126 Linear system 3 60 66 94 509 Linear transformation 40 100 Linear transformation, bijective 101 102 Linear transformation, determinant 121 Linear transformation, identity 103 Linear transformation, injective 102 Linear transformation, invariant 127 Linear transformation, nilpotent 134 Linear transformation, nullity 101 Linear transformation, orthogonal 441 Linear transformation, primary decomposition theorem 133 134 Linear transformation, principle of superposition 66 Linear transformation, projection 126 445 Linear transformation, range space 100 Linear transformation, reduced 127 Linear transformation, representation by a matrix 104 Linear transformation, spectral theorem 445 Linear transformation, spectrum 122 Linear transformation, surjective 101 102 Linearization 5 48 477 504 574 Linearization, examples 52 Linearized Equation 50 51 Linearly dependent 98 234 524 see Linearly independent 97 98 99 234 524 see Lipschitz condition 30 45 Lipschitz continuous 30 Lipscitz constant 30 45 LQG (linear quadratic Gaussian) problem 352 359 LQR (linear quadratic regulator) problem, continuous-time 342 LQR (linear quadratic regulator) problem, discrete-time 348 LU decomposition 647 Luenberger observer 351 Lyapunov function 468 491 Lyapunov function, construction of 474 500 Lyapunov function, level curve 471 Lyapunov matrix equation 468 469 499 Lyapunov stability 445 492 see Lyapunov stability, linear systems 452 495 see Lyapunov's direct method 468 Lyapunov's second method 468 Magnetic ball suspension 91 92 174—182 Mapping 8 see Markov parameter 204 387 399 Matrix 106 Matrix difference equation 496 Matrix differential equation 140 Matrix fractional description 517 521 see Matrix, block diagonal 128 Matrix, characteristic polynomial 123 Matrix, cofactor 113 Matrix, column 107 Matrix, column rank 119 Matrix, companion 461 Matrix, companion form 131 153 Matrix, condition number 646 647 649 Matrix, conformal 109 Matrix, congruent 436 Matrix, controllability 217 Matrix, cyclic 132 Matrix, determinant 111 113 Matrix, diagonal 120 Matrix, elementary unimodular 526 Matrix, eliminant 542 546 Matrix, exponential 57 149 150 Matrix, fundamental 139 140 Matrix, Gram 234 Matrix, Hamiltonian 344 349 Matrix, Hankel 399 Matrix, Hermite form 532 Matrix, hermitian 648 Matrix, highest degree coefficient 526 Matrix, Hurwitz 460 Matrix, idempotent 126 Matrix, identity 110 Matrix, ill-conditioned 647 Matrix, impulse response 77 166 Matrix, indefinite 443 Matrix, inverse 110 Matrix, Jacobian 48 447 Matrix, Jordan 130 135 136 Matrix, left inverse 653 Matrix, linear pencil 288 640 Matrix, logarithm 161 Matrix, lower triangular 131 Matrix, LU decomposition 647 Matrix, minimal polynomial 132 133 299 Matrix, minor 113 469 Matrix, modal 128 Matrix, Moore — Penrose inverse 652 Matrix, negative definite, semidefinite 443 469 Matrix, nilpotent 134 Matrix, nonsingular 101 110 Matrix, norm 43 Matrix, null 109 Matrix, observability 219 253 258 Matrix, orthogonal 441 648 Matrix, permutation of 112 Matrix, positive definite, semidefinite 443 Matrix, principal minor 113 469 Matrix, proper rational 391 Matrix, properties 107 Matrix, QR decomposition 647 Matrix, rank 101 107 306 437 524 525 Matrix, right inverse 653 Matrix, Rosenbrock 301 554 564 Matrix, self-adjoint 443 Matrix, singular 110 Matrix, Smith form 531 Matrix, square 107 Matrix, state transition 56 63 143 Matrix, Sylvester 541 Matrix, symmetric 469 648 Matrix, symmetric part 436 Matrix, system 301 554 564 Matrix, system, extended 557 Matrix, Toeplitz 259 Matrix, transfer function 78 168 178 Matrix, transpose 8 107 Matrix, unimodular 526 Matrix, unitary 648 Matrix, upper triangular 131 532 Matrix, well conditioned 647 Maximal element 27 Maximal element, Zorn's lemma 26 McMillan degree 397 Metric 438 Metric space 439 Microphone 84 MIMO system, multi input-multi output 66 71 Minimal basis 552 Minimal polynomial 132 133 299 Mode of system 156 157 186 187 see Model matching problem 374 633 644 Module, free 552 Monic polynomial 132 298 Moore — Penrose pseudo inverse 652 Motor, servomotor 14 206 380 Natural basis 100 see "Vector Negative, definite 437 469 491 see "Matrix" Negative, indefinite 469 see "Matrix" Negative, semidefinite 437 469 491 see "Matrix" Nilpotent operator 134 see Nonhomogeneous differential equations 138 145 see Nonlinear systems 3 451 477 Norm, Euclidean 42 Norm, Frobenius 653 Norm, induced 43 Norm, linear space 41 Norm, Manhattan 42 Norm, matrix 43 Norm, taxicab 42 Numerical solutions of algebraic equations 646 see Numerical solutions of differential equations 25 85 86 see Numerical stability 645 Observability 169 214 219 247 249 250 253 258 263 268 274 560 Observability, continuous-time system 248 252 Observability, discrete-time system 219 257 Observability, eigenvalue/eigenvector (PBH) test 272 Observability, gramian 249 253 259 Observability, index 295 Observability, matrix 219 253 258 Observability, subspace see "Unobservable" Observable 562 Observable eigenvalue 268 Observable mode 268 Observer companion form 203 Observer form 292 293 296 297 Observer form, multi-output 294 Observer form, single-input 293 Observer, Luenberger 351 see Open covering 18 Open loop control 327 Operator, linear 40 100 see Optimal control problem 342 348 Optimal estimation problem 352 357 359 362 Optimality principle 371 Orbit 492 Order of a realization 394 Orthogonal 439 Orthogonal basis 440 Orthogonal complement 441 Orthogonal linear transformation 441 Orthogonal matrix 441 648 Orthogonal projection 445 Orthonormal basis 439 Orthonormal set of vectors 439 Output feedback, dynamic 363 589 642 658 Output feedback, observer based 363 Output feedback, static 379 Output, decoupling zeros 302 564 Output, equation 5 58 61 Output, function controllability 313 Output, normal representations 430
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