Preface |
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vii | (8) |
Notation and Symbols |
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xv | (2) |
List of Acronyms |
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xvii | |
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1 | (10) |
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1.1 What Is This Book About? |
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1 | (2) |
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1.2 Highlights of This Book |
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3 | (6) |
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9 | (1) |
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10 | (1) |
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11 | (16) |
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11 | (1) |
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2.2 Eigenvalues and Eigenvectors |
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12 | (1) |
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2.3 Matrix Inversion Formulas |
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13 | (2) |
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15 | (1) |
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2.5 Vector Norms and Matrix Norms |
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16 | (3) |
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2.6 Singular Value Decomposition |
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19 | (4) |
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2.7 Semidefinite Matrices |
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23 | (1) |
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24 | (1) |
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24 | (3) |
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27 | (18) |
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3.1 Descriptions of Linear Dynamical Systems |
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27 | (1) |
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3.2 Controllability and Observability |
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28 | (3) |
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3.3 Observers and Observer-Based Controllers |
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31 | (3) |
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3.4 Operations on Systems |
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34 | (1) |
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3.5 State-Space Realizations for Transfer Matrices |
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35 | (3) |
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3.6 Multivariable System Poles and Zeros |
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38 | (3) |
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41 | (1) |
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42 | (3) |
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45 | (20) |
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45 | (2) |
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4.2 H(2) and H(XXX) Spaces |
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47 | (6) |
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4.3 Computing L(2) and H(2) Norms |
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53 | (2) |
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4.4 Computing L(XXX) and H(XXX) Norms |
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55 | (6) |
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61 | (1) |
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62 | (3) |
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65 | (16) |
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65 | (1) |
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5.2 Well-Posedness of Feedback Loop |
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66 | (2) |
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68 | (3) |
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5.4 Coprime Factorization over RH(XXX) |
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71 | (6) |
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77 | (1) |
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77 | (4) |
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6 Performance Specifications and Limitations |
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81 | (24) |
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81 | (4) |
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6.2 Weighted H(2) and H(XXX) Performance |
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85 | (4) |
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6.3 Selection of Weighting Functions |
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89 | (5) |
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6.4 Bode's Gain and Phase Relation |
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94 | (4) |
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6.5 Bode's Sensitivity Integral |
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98 | (2) |
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6.6 Analyticity Constraints |
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100 | (2) |
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102 | (1) |
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102 | (3) |
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7 Balanced Model Reduction |
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105 | (24) |
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106 | (1) |
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7.2 Balanced Realizations |
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107 | (10) |
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7.3 Model Reduction by Balanced Truncation |
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117 | (7) |
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7.4 Frequency-Weighted Balanced Model Reduction |
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124 | (2) |
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126 | (1) |
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127 | (2) |
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8 Uncertainty and Robustness |
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129 | (36) |
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129 | (8) |
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137 | (4) |
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8.3 Stability under Unstructured Uncertainties |
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141 | (6) |
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147 | (3) |
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8.5 Skewed Specifications |
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150 | (4) |
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8.6 Classical Control for MIMO Systems |
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154 | (3) |
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157 | (1) |
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158 | (7) |
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9 Linear Fractional Transformation |
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165 | (18) |
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9.1 Linear Fractional Transformations |
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165 | (8) |
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173 | (5) |
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9.3 Redheffer Star Products |
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178 | (2) |
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180 | (1) |
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181 | (2) |
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183 | (38) |
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10.1 General Framework for System Robustness |
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184 | (3) |
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10.2 Structured Singular Value |
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187 | (13) |
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10.3 Structured Robust Stability and Performance |
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200 | (13) |
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10.4 Overview of XXX Synthesis |
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213 | (3) |
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10.5 Notes and References |
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216 | (1) |
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217 | (4) |
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11 Controller Parameterization |
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221 | (12) |
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11.1 Existence of Stabilizing Controllers |
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222 | (2) |
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11.2 Parameterization of All Stabilizing Controllers |
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224 | (4) |
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11.3 Coprime Factorization Approach |
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228 | (3) |
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11.4 Notes and References |
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231 | (1) |
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231 | (2) |
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12 Algebraic Riccati Equations |
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233 | (20) |
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12.1 Stabilizing Solution and Riccati Operator |
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234 | (11) |
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245 | (1) |
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12.3 Notes and References |
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246 | (1) |
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246 | (7) |
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253 | (16) |
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13.1 Introduction to Regulator Problem |
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253 | (2) |
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13.2 Standard LQR Problem |
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255 | (3) |
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13.3 Extended LQR Problem |
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258 | (1) |
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13.4 Guaranteed Stability Margins of LQR |
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259 | (2) |
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13.5 Standard H(2) Problem |
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261 | (4) |
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13.6 Stability Margins of H(2) Controllers |
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265 | (2) |
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13.7 Notes and References |
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267 | (1) |
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267 | (2) |
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269 | (36) |
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269 | (1) |
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14.2 A Simplified H(XXX) Control Problem |
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270 | (12) |
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14.3 Optimality and Limiting Behavior |
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282 | (4) |
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14.4 Minimum Entropy Controller |
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286 | (1) |
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14.5 An Optimal Controller |
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286 | (2) |
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14.6 General H(XXX) Solutions |
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288 | (3) |
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14.7 Relaxing Assumptions |
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291 | (3) |
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14.8 H(2) and H(XXX) Integral Control |
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294 | (3) |
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297 | (2) |
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14.10 Notes and References |
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299 | (1) |
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300 | (5) |
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305 | (10) |
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15.1 H(XXX) Controller Reductions |
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306 | (6) |
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15.2 Notes and References |
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312 | (1) |
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313 | (2) |
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315 | (34) |
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16.1 Robust Stabilization of Coprime Factors |
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315 | (10) |
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325 | (3) |
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16.3 Justification for H(XXX) Loop Shaping |
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328 | (6) |
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16.4 Further Guidelines for Loop Shaping |
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334 | (7) |
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16.5 Notes and References |
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341 | (1) |
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342 | (7) |
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17 Gap Metric and v-Gap Metric |
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349 | (28) |
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350 | (7) |
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357 | (13) |
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17.3 Geometric Interpretation of v-Gap Metric |
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370 | (3) |
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17.4 Extended Loop-Shaping Design |
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373 | (2) |
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17.5 Controller Order Reduction |
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375 | (1) |
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17.6 Notes and References |
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375 | (1) |
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375 | (2) |
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377 | (14) |
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377 | (4) |
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18.2 Mixed XXX Analysis and Synthesis |
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381 | (8) |
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18.3 Notes and References |
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389 | (1) |
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390 | (1) |
Bibliography |
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391 | (16) |
Index |
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407 | |