CONTENTS 14.6 General Ho Solutions 14.7 Relaxing Assumptions 14.8 H2 and Hoo Integral Control 294 14.9 Hoo Filtering 14.10Notes and references 14.11 Problems 15 Controller reduction 15.1 Hoo Controller Reductions 15.2 Notes and references 12 15.3 Problems 16 Hoo Loop Shaping 16.1 Robust Stabilization of Coprime Factors 315 16.2 Loop-Shaping Design 325 16.3 Justification for Hoo Loop sha 16.4 Further Guidelines for Loop Shaping 16.5 Notes and references 341 16.6 Problems 342 17 Gap Metric and v-Gap Metric 349 17.1 Gap Metric 350 17.2 v-Gap Metric 17.3 Geometric Interpretation of v-Gap Metric 370 17.4 Extended Loop-Shaping Design 17.5 Controller Order Reduction 375 17.6 Notes and References 17.7 Problems 18 Miscellaneous Topics 377 18.1 Model Validation 18.2 Mixed u Analysis and Synthesis 18.3 Notes and References 18.4 Problems biography 391 Indexxiv CONTENTS 14.6 General H∞ Solutions ............................ 288 14.7 Relaxing Assumptions ............................ 291 14.8 H2 and H∞ Integral Control ........................ 294 14.9 H∞ Filtering ................................. 297 14.10Notes and References ............................. 299 14.11Problems ................................... 300 15 Controller Reduction 305 15.1 H∞ Controller Reductions .......................... 306 15.2 Notes and References ............................. 312 15.3 Problems ................................... 313 16 H∞ Loop Shaping 315 16.1 Robust Stabilization of Coprime Factors .................. 315 16.2 Loop-Shaping Design ............................. 325 16.3 Justification for H∞ Loop Shaping ..................... 328 16.4 Further Guidelines for Loop Shaping .................... 334 16.5 Notes and References ............................. 341 16.6 Problems ................................... 342 17 Gap Metric and ν-Gap Metric 349 17.1 Gap Metric .................................. 350 17.2 ν-Gap Metric ................................. 357 17.3 Geometric Interpretation of ν-Gap Metric ................. 370 17.4 Extended Loop-Shaping Design ....................... 373 17.5 Controller Order Reduction ......................... 375 17.6 Notes and References ............................. 375 17.7 Problems ................................... 375 18 Miscellaneous Topics 377 18.1 Model Validation ............................... 377 18.2 Mixed µ Analysis and Synthesis ....................... 381 18.3 Notes and References ............................. 389 18.4 Problems ................................... 390 Bibliography 391 Index 407