Introduction ix Chapter 1 The Loop-shaping Approach 1 1.1 Principle of the method 1 1.2 Generalized phase and gain margins 14 1.3 Limitations inherent to bandwidth 17 1.4 Examples 18 1.5 Conclusion 30 Chapter 2 Loop-shaping H Synthesis 33 2.1 The formalism of coprime factorizations 33 2.2 Robustness of normalized coprime factor plant descriptions 42 2.3 Explicit solution of the problem of robust stabilization of coprime factor plant descriptions 54 2.4 Robustness and -gap 77 2.5 Loop-shaping synthesis approach 82 2.6 Discrete approach 120 Chapter 3 Two Degrees-of-Freedom Controllers 135 31 Principle 135 3.2 Two-step approach 143 3.3 One-step approach 156 3.4 Comparison of the two approaches 165 3.5 Example 166 3.6 Compensation for a measurable disturbance at the model s output 174 Chapter 4 Extensions and Optimizations 187 4.1 Introduction 187 4.2 Fixed-order synthesis 188 4.4 Towards a new approach to loop-shaping fixed-order controller synthesis, etc 242 APPENDICES 245 Appendix 1 247 Appendix 2 251 Bibliography 255 Index 259
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