Computation and applications of the structured singular value
Abstract
IV 8 Non-Linear Systems 44 8 1 Linearisation 2 9 Sum m ary 3 N ew Algorithm 3 1 D ual Problem 3 1 1 A pplication of Geometric H ahn-Banach Theorem 3 2 O utline of the A lgorithm 3 2 1 O uter Loop 50 3 2 2 Inner Loop 3 3 Inner Loop Analysis and Some Suggested Improvements 53 3 3 1 The Linear Program (LP) 53 2 5 1 Statem ent of the Problem 36 3 3 2 CVD 56 vi 3 4 Improvements to the Basic Algorithm 60 3 4 1 Initialisation 60 3 4 2 M atrix Pencils 61 3 4 Tight C onstraints 64 3 5 Improvements with Real U ncertainty 68 3 6 Im plem entation of Changes to the Basic Algorithm 70 3 7 Proof of Convergence 3 8 Sum m ary 4 Algorithm Performance 77 4 1 R eliability of the Basic Algorithm 4 1 1 Complex U ncertainty 4 1 2 R eal/M ixed U ncertainty 4 1 3 Effect of Problem Size on Com puting Times 4 2 Improvements to the Basic Algorithm 4 2 1 Reliability 4 2 2 Accuracy 4 2 3 M ixed/Real U ncertainty 4 3 1-Norm Vs 2-Norm M ethods 92 4 3 1 T he Proxim ity Problem 92 4 3 2 Relaxing Accuracy Requirements 101
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