Linear Matrix Inequalities In System And Control Theory

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.

The underlying theory on which much modern robust and nonlinear control is based can be difficult to grasp. This volume is a collection of lecture notes presented by experts in advanced control engineering. The book is designed to provide a better grounding in the theory underlying several important areas of control. It is hoped the book will help the reader to apply otherwise abstruse ideas of nonlinear control in a variety of real systems.

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.

Although LMI has emerged as a powerful tool with applications across the major domains of systems and control, there has been a need for a textbook that provides an accessible introduction to LMIs in control systems analysis and design. Filling this need, LMIs in Control Systems: Analysis, Design and Applications focuses on the basic analysis and d

Control systems design methodologies have long suffered the traditional and myopic dichotomy between time and frequency domain approaches, each of them being specialized to cope with only scarcely overlapping performance requirements. This book is aimed at bridging the two approaches by presenting design methodologies based on the minimization of a norm (H2/H() of a suitable transfer function. A distinctive feature of these techniques is the fact that they do not create only one solution to the design problem, instead they provide a whole set of admissible solutions which satisfy a constraint on the maximum deterioration of the performance index. A systematic book on this topic is long overdue. Self-contained and practical in its approach, Control Theory and Design enables the reader to use the relevant techniques in various real-life applications. The text covers the basic facts of robustcontrol and theory as well as more recent achievements, such as robust stability and robust performance in presence of parameter uncertainties. It features a new perspective on classical LQC results and further sections on robust synthesis, nonclassicaloptimization problems, and analysis and synthesis of uncertain systems. Control Theory and Design is essential reading for graduates and those entering the research field. The required mathematical background is provided so that the book is also suitable for undergraduate students with some knowledge of basic systemsand control. Provides a self-contained manual for learning control systems and design Contains a clear and concise presentation of the technical background needed Includes a new perspective of classical LQG results Contains updated results and novel contributions to nonstandard RH2/RH infinity symbol problems Covers all the theory from the basic to the more advanced issues

This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor systems, such as dilated linear matrix inequality (LMI) characterizations for descriptor systems and performance control under regulation constraints. The second is a new path, which considers descriptor systems as a powerful tool for conceiving new control laws, understanding and deciphering some controller’s architecture and even homogenizing different—existing—ways of obtaining some new and/or known results for state-space systems. The book also highlights the comprehensive control problem for descriptor systems as an example of using the descriptor framework in order to transform a non-standard control problem into a classic stabilization control problem. In another section, an accurate solution is derived for the sensitivity constrained linear optimal control also using the descriptor framework. The book is intended for graduate and postgraduate students, as well as researchers in the field of systems and control theory.

Finite-time stability (FTS) is a more practical concept than classical Lyapunov stability, useful for checking whether the state trajectories of a system remain within pre-specified bounds over a finite time interval. In a linear systems framework, FTS problems can be cast as convex optimization problems and solved by the use of effective off-the-shelf computational tools such as LMI solvers. Finite-time Stability and Control exploits this benefit to present the practical applications of FTS and finite-time control-theoretical results to various engineering fields. The text is divided into two parts: · linear systems; and · hybrid systems. The building of practical motivating examples helps the reader to understand the methods presented. Finite-time Stability and Control is addressed to academic researchers and to engineers working in the field of robust process control. Instructors teaching graduate courses in advanced control will also find parts of this book useful for their courses.