Preface; Contents; Abbreviations; Part I Preliminaries; 1 Singular Perturbation Methods and Time-Scale Techniques; 1.1 Modelling; 1.1.1 Singularly Perturbed Phenomena; 1.1.2 Linear Time-Invariant Singularly Perturbed Systems; 1.1.3 Nonlinear Singularly Perturbed Systems; 1.1.4 Hybrid Singularly Perturbed Systems; 1.2 Time-Scale and Frequency-Scale Analysis; 1.2.1 Time-Scale and Multiple Time-Scales; 1.2.2 Multiple Frequency-Scales; 1.3 Slow-Fast Decomposition Method; 1.3.1 Decoupling Transformation; 1.3.2 Construction of Slow and Fast Subsystems; 1.4 Controllability and Observability

1.5 ConclusionReferences; 2 Theoretical Foundation of Finite Frequency Control; 2.1 The Laplace Transform; 2.2 Frequency Division Strategies; 2.2.1 Weighting Functions; 2.2.2 General Kalman-Yakubovich-Popov Lemma; 2.3 Characterization of Control Performance Index; 2.3.1 Characterization of Finite Frequency Ranges; 2.3.2 Window Norm; 2.3.3 Frequency Domain Inequalities; 2.4 Conclusion; References; Part II Singularly Perturbed Systems Analysis and Synthesis; 3 Stabilization of Singularly Perturbed Systems; 3.1 Stability Analysis of Dynamical Systems; 3.2 Stability Analysis and Integration

3.3 Stability Theory on Time Domain3.3.1 Method Based on Slow and Fast Subsystems; 3.3.2 A Descriptor-System Method; 3.4 Stability Theory on Frequency Domain; 3.5 Conclusion; References; 4 Finite Frequency Hinfty Control for Singularly Perturbed Systems; 4.1 Background Information for Hinfty Control of Singularly Perturbed Systems; 4.2 Finite Frequency Hinfty State Feedback Control; 4.3 Finite Frequency Hinfty Output Feedback Control; 4.3.1 The Slow Subsystem and Associated Hinfty Controller in the Low-Frequency Domain

4.3.2 The Fast Subsystem and Associated Controller in the High-Frequency Domain4.4 A Descriptor-System Approach for Hinfty Control of Singularly Perturbed Systems; 4.4.1 Shaping the High-Frequency Characteristics of a Singularly Perturbed Systems; 4.4.2 Shaping the Low-frequency Characteristics of a Singularly Perturbed Systems; 4.5 Finite Frequency Hinfty Tracking Problem; 4.6 Finite Frequency Hinfty Model Matching Problem; 4.7 Conclusion; References; 5 Finite Frequency Positive Real Control for Singularly Perturbed Systems; 5.1 Passivity and Positive Real Property

5.2 Methods Based on Slow-Fast Decomposition5.2.1 State Feedback Control for General Linear Systems; 5.2.2 Finite Frequency Positive Real Control for Singularly Perturbed Systems; 5.3 A Descriptor-System Method for Strictly Positive Real #x83;; 5.4 Conclusion; References; 6 The Sensitivity-Shaping Problem for Singularly Perturbed Systems; 6.1 Sensitivity Function and Complementary Sensitivity Function; 6.2 Finite Frequency S/T Mixed Sensitivity Design for SISO Singularly Perturbed Systems; 6.3 Finite Frequency H_/Hinfty Control for MIMO Singularly Perturbed Systems