Table of Contents
Preface vii
1 Decompositions of Large-Scale Systems 1
1.1 Epsilon Decompositions 1
1.2 The Decomposition Algorithm 6
1.3 Decompositions of Nonlinear Systems 9
1.4 Balanced BBD Decompositions 11
1.5 Input-Output Constrained Decompositions 18
Bibliography 25
2 Information Structure Constraints 29
2.1 Linear Matrix Inequalities: An Overview 29
2.2 Decentralized and BBD State Feedback 35
2.3 Turbine Governor Control 36
2.4 Low-Rank Corrections 39
2.4.1 Systems Where Decentralized LMI Design is Infeasible 41
2.4.2 Systems Where Decentralized LMI Design is Feasible 44
2.4.3 Implementation Issues 44
2.5 Low-Flank Corrections in Vehicle Control 45
2.6 Overlapping Control 47
2.6.1 Overlapping Control Design for Linear Systems 50
2.6.2 Overlapping Control of Nonlinear Systems 56
Bibliography 59
3 Algebraic Constraints on the Gain Matrix 65
3.1 Static Output Feedback 65
3.2 Arbitrary Information Structure Constraints 70
3.2.1 Preconditioning and Related Issues 71
3.3 Methods for Reducing Computational Complexity 79
3.3.1 Application to Large Flexible Structures 81
3.4 Applications to Large-Scale Lur'e Systems 85
3.4.1 The Design Algorithm 86
3.5 Control of Singular Systems 90
3.5.1 The Design Algorithm 94
3.5.2 Applications to Nonlinear Circuits 102
Bibliography 105
4 Regions of Attraction 111
4.1 Generalized Bounding Procedures 113
4.2 Uncertain Systems 119
4.3 Large Sparse Systems 123
4.4 Exciter Control 129
Bibliography 139
5 Parametric Stability 143
5.1 Parametric Stabilization Using LMIs 144
5.2 Selection of the Reference Input 147
5.3 Parametrically-Dependent Control Laws 149
5.4 Extensions to a General Class of Nonlinearities 155
Bibliography 162
6 Future Directions: Dynamic Graphs 165
6.1 Control of Dynamic Graphs 166
6.2 Generalized Dynamic Graphs 174
6.3 Continuous Boolean Networks 178
6.4 Applications to Gene Regulation 183
6.4.1 Protein Dynamics 184
6.4.2 Gene Dynamics 185
6.5 Entangled Graphs 192
6.6 Dynamic Properties of Entangled Graphs 196
6.6.1 Computational Considerations 197
6.6.2 Stability and Related Issues 200
6.7 Structural Models for Entangled Graphs 204
6.7.1 Cloning and Embedding 204
6.7.2 Self-Replication and Random Mutations 206
6.8 Applications to Large-Scale Boolean Networks 209
Bibliography 213
Index 217
