This book presents recent research on the stability analysis of polynomial-fuzzy-model-based control systems where the concept of partially/imperfectly matched premises and membership-function dependent analysis are considered. The membership-function-dependent analysis offers a new research direction for fuzzy-model-based control systems by taking into account the characteristic and information of the membership functions in the stability analysis. The book presents on a research level the most recent and advanced research results, promotes the research of polynomial-fuzzy-model-based control systems, and provides theoretical support and point a research direction to postgraduate students and fellow researchers. Each chapter provides numerical examples to verify the analysis results, demonstrate the effectiveness of the proposed polynomial fuzzy control schemes, and explain the design procedure. The book is comprehensively written enclosing detailed derivation steps and mathematical derivations also for readers without extensive knowledge on the topics including students with control background who are interested in polynomial fuzzy model-based control systems.

The main research objective in this thesis is to investigate the stability and performance of the interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) control system. PFMB control scheme has been developed recently around 2009 and demonstrates more potential than the traditional Takagi-Sugeno fuzzy-model-based (T-S FMB) control approach to represent the nonlinearities in the plant. Meanwhile, the IT2 fuzzy logic has also been proposed to incorporate uncertainties of the nonlinear systems into the membership functions directly. Through the IT2 PFMB control design approach, both the nonlinearity and the uncertainty in the system can be handled well. The control performance and the relaxation of stability conditions of IT2 PFMB control systems are studied and investigated in the thesis. The main contribution of the thesis is summarized in three tasks and presented as following: In the first task in Chapter 3, the stability conditions of the PFMB systems equipped with mismatched IT2 membership functions are investigated. Unlike the membership-function-independent (MFI) methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own merits, are proposed to conduct the stability analysis for the IT2 PFMB control systems and all of the methods can achieve feasible control results. All the three approaches are well explained, which offers the reader systematic ways to include the information of the membership functions into the analysis. In addition, all the approaches are compared and the pros and cons are presented to help the reader choose the most appropriate approach in the applications.

In this book, the state-of-the-art fuzzy-model-based (FMB) based control approaches are covered. A comprehensive review about the stability analysis of type-1 and type-2 FMB control systems using the Lyapunov-based approach is given, presenting a clear picture to researchers who would like to work on this field. A wide variety of continuous-time nonlinear control systems such as state-feedback, switching, time-delay and sampled-data FMB control systems, are covered. In short, this book summarizes the recent contributions of the authors on the stability analysis of the FMB control systems. It discusses advanced stability analysis techniques for various FMB control systems, and founds a concrete theoretical basis to support the investigation of FMB control systems at the research level. The analysis results of this book offer various mathematical approaches to designing stable and well-performed FMB control systems. Furthermore, the results widen the applicability of the FMB control approach and help put the fuzzy controller in practice. A wide range of advanced analytical and mathematical analysis techniques will be employed to investigate the system stability and performance of FMB-based control systems in a rigorous manner. Detailed analysis and derivation steps are given to enhance the readability, enabling the readers who are unfamiliar with the FMB control systems to follow the materials easily. Simulation examples, with figures and plots of system responses, are given to demonstrate the effectiveness of the proposed FMB control approaches.

In this book, the state-of-the-art fuzzy-model-based (FMB) based control approaches are covered. A comprehensive review about the stability analysis of type-1 and type-2 FMB control systems using the Lyapunov-based approach is given, presenting a clear picture to researchers who would like to work on this field. A wide variety of continuous-time nonlinear control systems such as state-feedback, switching, time-delay and sampled-data FMB control systems, are covered. In short, this book summarizes the recent contributions of the authors on the stability analysis of the FMB control systems. It discusses advanced stability analysis techniques for various FMB control systems, and founds a concrete theoretical basis to support the investigation of FMB control systems at the research level. The analysis results of this book offer various mathematical approaches to designing stable and well-performed FMB control systems. Furthermore, the results widen the applicability of the FMB control approach and help put the fuzzy controller in practice. A wide range of advanced analytical and mathematical analysis techniques will be employed to investigate the system stability and performance of FMB-based control systems in a rigorous manner. Detailed analysis and derivation steps are given to enhance the readability, enabling the readers who are unfamiliar with the FMB control systems to follow the materials easily. Simulation examples, with figures and plots of system responses, are given to demonstrate the effectiveness of the proposed FMB control approaches.

A comprehensive treatment of model-based fuzzy control systems This volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Building on the Takagi-Sugeno fuzzy model, authors Tanaka and Wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of performance specifications, numerical implementations, and practical applications. Issues that have not been fully treated in existing texts, such as stability analysis, systematic design, and performance analysis, are crucial to the validity and applicability of fuzzy control methodology. Fuzzy Control Systems Design and Analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model. This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities (LMI) as an approach to fuzzy design and control. It also covers advanced topics in model-based fuzzy control systems, including modeling and control of chaotic systems. Later sections offer practical examples in the form of detailed theoretical and experimental studies of fuzzy control in robotic systems and a discussion of future directions in the field. Fuzzy Control Systems Design and Analysis offers an advanced treatment of fuzzy control that makes a useful reference for researchers and a reliable text for advanced graduate students in the field.

In this thesis using fuzzy logic methodology, the stability of complex nonlinear control systems is investigated. Fuzzy-Model-Based (FMB) control system offers a systematic platform in handling control problems from the point of view of stability analysis. In this platform, Membership Functions (MFs) gather the overall nonlinear properties of the control system. The lack of the information of MFs is one the main sources of conservativeness in the current stability analysis approaches. To widen the applicability of the FMB control scheme, the aim of the proposed research the¬sis is to derive less conservative stability conditions. Therefore, some attempts are made to obtain relaxed shape-dependent stability conditions. The results of this investigation are presented in three parts as follows: 1. The stability analysis of FMB control systems under Parallel Distributed Com¬ pensation (PDC) is carried out. First, the stability conditions, which are the inequal¬ ities in the form of p-dimensional fuzzy summation, are expanded to n-dimensional fuzzy summation (n > p). The global and regional boundary information of MFs are then utilized for relaxation of stability analysis results and two analysis approaches are proposed namely Global-Membership-Function-Shape-Dependent (GMFSD) ap¬ proach and Regional-Membership-Function-Shape-Dependent (RMFSD) approach, respectively. For RMFSD approach the operating region is partitioned into subre- glons and the boundary information of MFs on all operating subregions are employed to facilitate the stability analysis. The stability conditions are derived in the form of Linear Matrix Inequality (LMI). 2. Employing Sum of Squares (SOS) approach, relaxed stability conditions for Polynomial-Fuzzy-Model-Based (PFMB) control systems are derived. First, MFs are approximated by some polynomials in the partitioned operating domain of MFs.