Authors |
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vii | (2) |
Preface |
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ix | (4) |
Introduction |
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xiii | |
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1 Mathematical Background |
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1 | (56) |
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1 | (1) |
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1.2 Metric Spaces and Contraction Mapping Theory |
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1 | (17) |
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2 | (7) |
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1.2.2 Mappings in Metric Spaces |
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9 | (5) |
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1.2.3 Contraction Mappings and Fixed Points |
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14 | (4) |
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1.3 Some Properties of Vectors and Matrices |
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18 | (35) |
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1.3.1 Norms of Vectors and Matrices |
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18 | (12) |
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1.3.2 Special Matrix Forms |
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30 | (11) |
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41 | (12) |
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53 | (4) |
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2 Mathematics of Dynamic Processes |
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57 | (50) |
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2.1 Solution of Ordinary Differential Equations |
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57 | (32) |
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2.1.1 Existence and Uniqueness Theorems |
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57 | (8) |
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2.1.2 Solution of Linear Differential Equations |
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65 | (10) |
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75 | (14) |
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2.2 Solution of Difference Equations |
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89 | (14) |
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89 | (3) |
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2.2.2 Solution of Linear Difference Equations |
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92 | (3) |
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95 | (8) |
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103 | (4) |
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3 Characterization of Systems |
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107 | (90) |
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3.1 The Concept of Dynamic Systems |
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107 | (5) |
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3.2 Equilibrium and Linearization |
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112 | (7) |
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3.3 Continuous Linear Systems |
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119 | (25) |
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3.3.1 State-Space Approach |
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119 | (2) |
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121 | (4) |
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3.3.3 Equations in Input-Output Form |
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125 | (4) |
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129 | (11) |
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3.3.5 Adjoint and Dual Systems |
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140 | (4) |
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144 | (5) |
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149 | (42) |
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3.5.1 Dynamic Systems in Engineering |
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149 | (24) |
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3.5.2 Dynamic Systems in Social Sciences |
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173 | (18) |
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191 | (6) |
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197 | (46) |
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4.1 The Elements of the Lyapunov Stability Theory |
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198 | (21) |
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199 | (6) |
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4.1.2 The stability of time-variant linear systems |
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205 | (1) |
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4.1.3 The Stability of Time-Invariant Linear Systems |
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206 | (13) |
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219 | (5) |
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224 | (14) |
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4.3.1 Applications in Engineering |
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224 | (5) |
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4.3.2 Applications in the Social Sciences |
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229 | (9) |
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238 | (5) |
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243 | (50) |
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243 | (25) |
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244 | (12) |
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5.1.2 Time-Invariant Systems |
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256 | (8) |
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5.1.3 Output and Trajectory Controllability |
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264 | (4) |
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268 | (6) |
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274 | (13) |
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5.3.1 Dynamic Systems in Engineering |
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274 | (7) |
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5.3.2 Applications in the Social Sciences |
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281 | (6) |
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287 | (6) |
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293 | (34) |
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294 | (9) |
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294 | (5) |
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6.1.2 Time-Invariant Systems |
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299 | (4) |
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303 | (4) |
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307 | (3) |
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310 | (12) |
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6.4.1 Dynamic Systems in Engineering |
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310 | (6) |
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6.4.2 Applications in the Social Sciences |
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316 | (6) |
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322 | (5) |
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327 | (48) |
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7.1 Diagonal and Jordan Forms |
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329 | (4) |
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7.2 Controllability Canonical Forms |
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333 | (9) |
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7.3 Observability Canonical Forms |
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342 | (4) |
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346 | (23) |
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7.4.1 Dynamic Systems in Engineering |
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346 | (14) |
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7.4.2 Applications in the Social Sciences and Economics |
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360 | (9) |
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369 | (6) |
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375 | (50) |
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8.1 Realizability of Weighting Patterns |
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376 | (20) |
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8.1.1 Realizability Conditions |
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377 | (3) |
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8.1.2 Minimal Realizations |
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380 | (7) |
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8.1.3 Time-Invariant Realizations |
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387 | (9) |
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8.2 Realizability of Transfer Functions |
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396 | (11) |
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8.2.1 Realizability Conditions |
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397 | (7) |
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8.2.2 Minimal Realizations |
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404 | (3) |
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407 | (12) |
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8.3.1 Dynamic Systems in Engineering |
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407 | (5) |
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8.3.2 Applications in the Social Sciences and Economics |
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412 | (7) |
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419 | (6) |
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425 | (38) |
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9.1 The Eigenvalue Placement Theorem |
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426 | (5) |
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431 | (4) |
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9.3 Reduced-Order Observers |
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435 | (2) |
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9.4 The Eigenvalue Separation Theorem |
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437 | (4) |
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441 | (16) |
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9.5.1 Dynamic Systems in Engineering |
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441 | (9) |
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9.5.2 Applications in the Social Sciences and Economics |
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450 | (7) |
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457 | (6) |
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463 | (36) |
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463 | (6) |
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10.2 The Kalman-Bucy Filter |
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469 | (3) |
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10.3 Adaptive Control Systems |
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472 | (12) |
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484 | (15) |
References |
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499 | (4) |
Index |
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503 | |