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Table of Contents
Preface; Part I Introduction and Preliminaries; Part II Stability Analysis Techniques; Part III Advanced Control Methodologies; Part IV Advanced Lyapunov Functions; Acknowledgments; Contents; Acronyms; Part I Introduction and Preliminaries; 1 Introduction; 1.1 Background; 1.2 Fuzzy Model-Based Control; 1.2.1 Fuzzy Models; 1.2.2 Fuzzy Controllers; 1.2.3 Other Fuzzy Controllers; 1.3 Stability Analysis; 1.3.1 Types of Lyapunov Functions; 1.3.2 Types of Stability Analysis; 1.3.3 Techniques of Stability Analysis; 1.4 Control Problems; 1.4.1 Stabilization Control Problem
1.4.2 Regulation Control Problem1.4.3 Tracking Control Problem; 1.5 Design of FMB Control Systems; 1.6 Conclusion; References; 2 Preliminaries; 2.1 Introduction; 2.2 Notation; 2.3 Fuzzy Models; 2.3.1 T-S Fuzzy Model; 2.3.2 Polynomial Fuzzy Model; 2.4 State-Feedback Fuzzy Controller; 2.4.1 Fuzzy Controller; 2.4.2 Polynomial Fuzzy Controller; 2.5 Various Types of FMB Control Systems; 2.5.1 FMB Control System; 2.5.2 PFMB Control System; 2.6 LMI/SOS-Based Stability Conditions; 2.6.1 LMI-Based Stability Conditions for FMB Control Systems
2.6.2 SOS-Based Stability Conditions for FMB Control Systems2.7 Conclusion; References; Part II Stability Analysis Techniques; 3 Stability Analysis of Polynomial Fuzzy Model-Based Control Systems with Mismatched Premise Membership Functions Through Symbolic Variables; 3.1 Introduction; 3.2 Stability Analysis; 3.2.1 Property of Membership Functions; 3.2.2 Boundary Information of Membership Grades; 3.2.3 Boundary Information of Premise Variables; 3.3 Simulation Example; 3.4 Conclusion; References
4 Stability Analysis of Polynomial Fuzzy Model-Based Control Systems with Mismatched Premise Membership Functions Through Taylor Series Membership Functions4.1 Introduction; 4.2 Taylor Series Membership Functions; 4.3 Stability Analysis; 4.4 Simulation Example; 4.5 Conclusion; References; 5 Stability Analysis of General Polynomial Fuzzy Model-Based Control Systems; 5.1 Introduction; 5.2 Stability Analysis; 5.2.1 Perfectly Matched Premises; 5.2.2 Partially Matched Premises; 5.2.3 Imperfectly Matched Premises; 5.3 Simulation Example; 5.3.1 Perfectly Matched Premises
5.3.2 Partially Matched Premises5.3.3 Imperfectly Matched Premises; 5.4 Conclusion; References; Part III Advanced Control Methodologies; 6 Output Regulation of Polynomial Fuzzy Model-Based Control Systems; 6.1 Introduction; 6.2 Preliminaries; 6.2.1 Polynomial Fuzzy Model with Output; 6.2.2 Polynomial Fuzzy Controller with Integral Action; 6.2.3 PFMB Control System; 6.3 Stability Analysis; 6.3.1 Perfectly Matched Premises; 6.3.2 Perfectly Matched Premise with Regional Membership Function Information; 6.3.3 Partially Matched Premises; 6.3.4 Imperfectly Matched Premises; 6.4 Simulation Example
1.4.2 Regulation Control Problem1.4.3 Tracking Control Problem; 1.5 Design of FMB Control Systems; 1.6 Conclusion; References; 2 Preliminaries; 2.1 Introduction; 2.2 Notation; 2.3 Fuzzy Models; 2.3.1 T-S Fuzzy Model; 2.3.2 Polynomial Fuzzy Model; 2.4 State-Feedback Fuzzy Controller; 2.4.1 Fuzzy Controller; 2.4.2 Polynomial Fuzzy Controller; 2.5 Various Types of FMB Control Systems; 2.5.1 FMB Control System; 2.5.2 PFMB Control System; 2.6 LMI/SOS-Based Stability Conditions; 2.6.1 LMI-Based Stability Conditions for FMB Control Systems
2.6.2 SOS-Based Stability Conditions for FMB Control Systems2.7 Conclusion; References; Part II Stability Analysis Techniques; 3 Stability Analysis of Polynomial Fuzzy Model-Based Control Systems with Mismatched Premise Membership Functions Through Symbolic Variables; 3.1 Introduction; 3.2 Stability Analysis; 3.2.1 Property of Membership Functions; 3.2.2 Boundary Information of Membership Grades; 3.2.3 Boundary Information of Premise Variables; 3.3 Simulation Example; 3.4 Conclusion; References
4 Stability Analysis of Polynomial Fuzzy Model-Based Control Systems with Mismatched Premise Membership Functions Through Taylor Series Membership Functions4.1 Introduction; 4.2 Taylor Series Membership Functions; 4.3 Stability Analysis; 4.4 Simulation Example; 4.5 Conclusion; References; 5 Stability Analysis of General Polynomial Fuzzy Model-Based Control Systems; 5.1 Introduction; 5.2 Stability Analysis; 5.2.1 Perfectly Matched Premises; 5.2.2 Partially Matched Premises; 5.2.3 Imperfectly Matched Premises; 5.3 Simulation Example; 5.3.1 Perfectly Matched Premises
5.3.2 Partially Matched Premises5.3.3 Imperfectly Matched Premises; 5.4 Conclusion; References; Part III Advanced Control Methodologies; 6 Output Regulation of Polynomial Fuzzy Model-Based Control Systems; 6.1 Introduction; 6.2 Preliminaries; 6.2.1 Polynomial Fuzzy Model with Output; 6.2.2 Polynomial Fuzzy Controller with Integral Action; 6.2.3 PFMB Control System; 6.3 Stability Analysis; 6.3.1 Perfectly Matched Premises; 6.3.2 Perfectly Matched Premise with Regional Membership Function Information; 6.3.3 Partially Matched Premises; 6.3.4 Imperfectly Matched Premises; 6.4 Simulation Example