1 Introduction |
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1 | (6) |
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5 | (2) |
2 Preliminaries |
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7 | (30) |
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2.1 Linear Algebra and Matrix Theory |
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7 | (9) |
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2.1.1 Vectors and Matrices |
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7 | (3) |
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10 | (1) |
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2.1.3 Eigenvalues and Eigenvectors |
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11 | (1) |
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2.1.4 Matrix Inversion and Pseudoinverse |
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12 | (2) |
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2.1.5 Vector Norms and Matrix Norms |
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14 | (1) |
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2.1.6 Singular Value Decomposition |
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15 | (1) |
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2.2 Function Spaces and Signals |
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16 | (6) |
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16 | (3) |
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2.2.2 Norms for Signals and Systems |
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19 | (3) |
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22 | (9) |
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22 | (1) |
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2.3.2 State Similarity Transformation |
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23 | (1) |
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2.3.3 Stability, Controllability, and Observability |
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24 | (2) |
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2.3.4 Minimal State-Space Realization |
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26 | (1) |
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2.3.5 State-Space Algebra |
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27 | (1) |
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2.3.6 State-Space Formula for Parallel Systems |
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28 | (1) |
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2.3.7 State-Space Formula for Cascaded Systems |
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29 | (1) |
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2.3.8 State-Space Formula for Similarity Transformation |
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29 | (2) |
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2.4 Linear Fractional Transformations and Chain Scattering-Matrix Description |
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31 | (3) |
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34 | (1) |
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35 | (2) |
3 Two-Port Networks |
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37 | (28) |
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3.1 One-Port and Two-Port Networks |
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37 | (3) |
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3.2 Impedance and Admittance Parameters (Z and Y Parameters) |
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40 | (3) |
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3.3 Hybrid Parameters (H Parameters) |
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43 | (1) |
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3.4 Transmission Parameters (ABCD Parameters) |
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44 | (4) |
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3.5 Scattering Parameters (S Parameters) |
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48 | (3) |
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3.6 Chain Scattering Parameters (T Parameters) |
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51 | (3) |
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3.7 Conversions Between (ABCD) and (S, T) Matrix Parameters |
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54 | (1) |
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55 | (6) |
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61 | (2) |
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63 | (2) |
4 Linear Fractional Transformations |
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65 | (34) |
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4.1 Linear Fractional Transformations |
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65 | (4) |
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4.2 Application of LFT in State-Space Realizations |
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69 | (5) |
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4.3 Examples of Determining LFT Matrices |
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74 | (6) |
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75 | (1) |
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76 | (1) |
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76 | (4) |
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4.4 Relationship Between Mason's Gain Formulae and LFT |
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80 | (9) |
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4.5 LFT Description and Feedback Controllers |
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89 | (3) |
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4.6 Inner and Co-inner Systems |
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92 | (3) |
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95 | (2) |
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97 | (2) |
5 Chain Scattering Descriptions |
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99 | (46) |
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5.1 CSD Definitions and Manipulations |
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99 | (4) |
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5.2 Cascaded Connection of Two CSD Matrices |
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103 | (4) |
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5.3 Transformation from LFT to CSD Matrix |
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107 | (3) |
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5.4 Transformation from LFT to Cascaded CSDs |
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110 | (5) |
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5.5 Transformation from CSD to LFT matrix |
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115 | (6) |
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5.6 Applications of CSDs in State-Space Realizations |
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121 | (6) |
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5.7 An Application of CSDs to Similarity Transformations |
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127 | (1) |
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5.8 State-Space Formulae of CSD Matrix Transformed from LFT Matrix |
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128 | (3) |
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5.9 State-Space Formulae of LFT Matrix Transformed from CSD Matrix |
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131 | (3) |
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134 | (2) |
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5.11 J-Lossless and Dual J-Lossless Systems |
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136 | (5) |
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141 | (2) |
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143 | (2) |
6 Coprime Factorizations |
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145 | (26) |
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6.1 Coprimeness and Coprime Factorization |
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145 | (3) |
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6.2 Coprime Factorization over RHinfinity |
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148 | (20) |
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6.3 Normalized Coprime Factorization |
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168 | (2) |
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170 | (1) |
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170 | (1) |
7 Algebraic Riccati Equations and Spectral Factorizations |
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171 | (40) |
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7.1 Algebraic Riccati Equations |
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171 | (7) |
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7.2 Similarity Transformation of Hamiltonian Matrices |
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178 | (5) |
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183 | (2) |
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7.4 State-Space Formulae for Spectral Factorizations Using Coprime Factorization Approach |
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185 | (23) |
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7.4.1 Spectral Factorization Case I |
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188 | (10) |
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7.4.2 Spectral Factorization Case II |
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198 | (5) |
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7.4.3 Spectral Factorization Case III |
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203 | (5) |
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208 | (1) |
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209 | (2) |
8 CSD Approach to Stabilization Control and H2 Optimal Control |
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211 | (56) |
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212 | (1) |
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8.2 Characterization of All Stabilizing Controllers |
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213 | (7) |
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8.2.1 Method I: CSDr CSDl Using a Right CSD Coupled with a Left CSD |
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214 | (3) |
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8.2.2 Method II: CSDl CSDr Using a Left CSD Coupled with a Right CSD |
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217 | (3) |
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8.3 State-Space Formulae of Stabilizing Controllers |
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220 | (7) |
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8.3.1 Method I: CSDr CSDl |
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220 | (4) |
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8.3.2 Method II: CSD1 CSDr, |
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224 | (3) |
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8.4 Example of Finding Stabilizing Controllers |
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227 | (8) |
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8.4.1 Method I: CSDr CSDl Using a Right CSD Associated with a Left CSD |
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228 | (4) |
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8.4.2 Method II: CSDl CSDr Using a Left CSD Associated with a Right CSD |
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232 | (3) |
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8.5 Stabilization of Special SCC Formulations |
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235 | (12) |
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8.5.1 Disturbance Feedforward (DF) Case |
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237 | (1) |
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8.5.2 Full Information (FI) Case |
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238 | (1) |
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8.5.3 State Feedback (SF) Case |
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239 | (1) |
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8.5.4 Output Estimation (OE) Case |
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240 | (2) |
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8.5.5 Full Control (FC) Case |
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242 | (1) |
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8.5.6 Output Injection (OI) Case |
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243 | (4) |
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8.6 Optimal H2 Controller |
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247 | (5) |
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8.6.1 Method I: Using a Right CSD Associated with a Left One |
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248 | (3) |
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8.6.2 Method II: Using a Left CSD Associated with a Right One |
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251 | (1) |
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8.7 Example of the Output Feedback H2 Optimal Control Problem |
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252 | (5) |
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8.7.1 A Numerical Example |
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254 | (3) |
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8.8 Example of LQR Controller |
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257 | (2) |
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8.9 More Numerical Examples |
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259 | (5) |
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264 | (1) |
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264 | (3) |
9 A CSD Approach to H-Infinity Controller Synthesis |
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267 | (36) |
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268 | (6) |
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9.1.1 Method I: CSDr CSDl Right CSD Coupled with Left CSD |
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269 | (2) |
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9.1.2 Method II: CSDl CSDr Left CSD Coupled with Right CSD |
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271 | (3) |
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9.2 State-Space Formulae of HInfinity Controllers |
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274 | (7) |
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9.2.1 Method I: CSDr CSDl |
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274 | (4) |
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9.2.2 Method II: CSDl CSDl |
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278 | (3) |
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9.3 Hinfinity Solution of Special SCC Formulations |
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281 | (9) |
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9.3.1 Disturbance Feedforward (DF) Problem |
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281 | (2) |
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9.3.2 Full Information (FI) Problem |
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283 | (2) |
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9.3.3 State Feedback (SF) Problem |
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285 | (1) |
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9.3.4 Output Estimation (OE) Problem |
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285 | (2) |
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9.3.5 Full Control (FC) Problem |
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287 | (2) |
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9.3.6 Output Injection (OI) Problem |
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289 | (1) |
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9.4 Hinfinity Controller Synthesis with Coprime Factor Perturbations |
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290 | (11) |
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9.4.1 Robust Stabilization Problem of Left Coprime Factorization Case |
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291 | (5) |
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9.4.2 Robust Stabilization Problem of Right Coprime Factor Case |
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296 | (5) |
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301 | (1) |
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301 | (2) |
10 Design Examples |
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303 | (30) |
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10.1 Mathematical Models of DC Servomotor |
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303 | (1) |
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10.2 Two-Port Chain Description Approach to Estimation of Mechanical Loading |
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304 | (8) |
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10.3 Coprime Factorization Approach to System Identification |
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312 | (2) |
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10.4 Hoc, Robust Controller Design for Speed Control |
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314 | (17) |
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314 | (7) |
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321 | (2) |
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10.4.3 Coprime Factorization Approach to Advanced PDFF Controller |
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323 | (8) |
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331 | (1) |
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331 | (2) |
Index |
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333 | |