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vi CONTENTS
3.5 SystemInterconnection ............................ 91
3.6 H
2
and H
∞
AnalysisandSynthesis...................... 95
3.6.1 ControllerSynthesis .......................... 95
3.6.2 SystemNormCalculations ...................... 105
3.7 Structured Singular Value (µ) Analysis and Synthesis . . . . . . . . . . . 107
3.7.1 Calculation of µ ............................ 107
3.7.2 The D-K Iteration........................... 110
3.7.3 Fitting D Scales ............................ 112
3.7.4 Constructing Rational Perturbations . . . . . . . . . . . . . . . . . 120
3.7.5 BlockStructuredNormCalculations................. 121
3.8 ModelReduction................................ 121
3.8.1 Truncation and Residualization . . . . . . . . . . . . . . . . . . . . 122
3.8.2 BalancedRealizations ......................... 123
3.8.3 Hankel Singular Value Approximation . . . . . . . . . . . . . . . . 125
4 Demonstration Examples 127
4.1 TheHimatExample .............................. 127
4.1.1 ProblemDescription.......................... 127
4.1.2 State-spaceModelofHimat...................... 128
4.1.3 Creating a Weighted Interconnection Structure for Design . . . . . 131
4.1.4 H
∞
Design ............................... 133