Stability Analysis and Design for Nonlinear Singular Systems
Stability Analysis and Design for Nonlinear Singular Systems

Author: Chunyu Yang

Publisher: Springer

Published: 2012-08-14

Total Pages: 213

ISBN-13: 3642321445

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Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability for standard state-space systems were generalized to singular systems. For Lur’e type descriptor systems (LDS) which were the feedback interconnection of a descriptor system with a static nonlinearity, strongly absolute stability was defined and Circle criterion and Popov criterion were derived. The notion of input-state stability (ISS) for nonlinear singular systems was defined based on the concept of ISS for standard state-space systems and the characteristics of singular systems. LMI-based sufficient conditions for ISS of Lur’e singular systems were proposed. Furthermore, observer design for nonlinear singular systems was studied and some observer design methods were proposed by the obtained stability results and convex optimization algorithms. Finally, absolute stability and multi-objective control of nonlinear singularly perturbed systems were considered. By Lyapunov functions, absolute stability criteria of Lur’e singularly perturbed systems were proposed and multi-objective control of T-S fuzzy singularly perturbed systems was achieved. Compared with the existing results, the obtained methods do not depend on the decomposition of the original system and can produce a determinate upper bound for the singular perturbation parameter.

Nonlinear Systems Analysis
Nonlinear Systems Analysis

Author: M. Vidyasagar

Publisher: SIAM

Published: 2002-01-01

Total Pages: 515

ISBN-13: 9780898719185

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When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.

Unsolved Problems in Mathematical Systems and Control Theory
Unsolved Problems in Mathematical Systems and Control Theory

Author: Vincent D. Blondel

Publisher: Princeton University Press

Published: 2009-04-11

Total Pages: 351

ISBN-13: 1400826152

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This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

Analysis and Design of Descriptor Linear Systems
Analysis and Design of Descriptor Linear Systems

Author: Guang-Ren Duan

Publisher: Springer Science & Business Media

Published: 2010-09-14

Total Pages: 504

ISBN-13: 1441963979

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Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory. The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory.

Robust Control and Filtering of Singular Systems
Robust Control and Filtering of Singular Systems

Author: Shengyuan Xu

Publisher: Lecture Notes in Control and Information Sciences

Published: 2006-04-21

Total Pages: 256

ISBN-13:

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Singular systems have been widely studied in the past two decades due to their extensive applications in modelling and control of electrical circuits, power systems, economics and other areas. Interest has grown recently in the stability analysis and control of singular systems with parameter uncertainties due to their frequent presence in dynamic systems, which is much more complicated than that of state-space systems because controllers must be designed so that the closed-loop system is not only robustly stable, but also regular and impulse-free (in the continuous case) or causal (in the discrete case), while the latter two issues do not arise in the state-space case. This monograph aims to present up-to-date research developments and references on robust control and filtering of uncertain singular systems in a unified matrix inequality setting. It provides a coherent approach to studying control and filtering problems as extensions of state-space systems without the commonly used slow-fast decomposition. It contains valuable reference material for researchers wishing to explore the area of singular systems, and its contents are also suitable for a one-semester graduate course.

Design of Nonlinear Control Systems with the Highest Derivative in Feedback
Design of Nonlinear Control Systems with the Highest Derivative in Feedback

Author: Valery D. Yurkevich

Publisher: World Scientific

Published: 2004

Total Pages: 376

ISBN-13: 9812388990

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This unique book presents an analytical uniform design methodology of continuous-time or discrete-time nonlinear control system design which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances. All results are illustrated with numerical simulations, their practical importance is highlighted, and they may be used for real-time control system design in robotics, mechatronics, chemical reactors, electrical and electro-mechanical systems as well as aircraft control systems. The book is easy reading and is suitable for teaching.

Applied Nonlinear Control
Applied Nonlinear Control

Author: Jean-Jacques E. Slotine

Publisher:

Published: 1991

Total Pages: 461

ISBN-13: 9780130400499

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In this work, the authors present a global perspective on the methods available for analysis and design of non-linear control systems and detail specific applications. They provide a tutorial exposition of the major non-linear systems analysis techniques followed by a discussion of available non-linear design methods.

Large-Scale Fuzzy Interconnected Control Systems Design and Analysis
Large-Scale Fuzzy Interconnected Control Systems Design and Analysis

Author: Zhong, Zhixiong

Publisher: IGI Global

Published: 2017-05-17

Total Pages: 235

ISBN-13: 1522523863

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Large-scale interconnected systems have become more prominent in society due to a higher demand for sustainable development. As such, it is imperative to create effective methods and techniques to control such systems. Large-Scale Fuzzy Interconnected Control Systems Design and Analysis is an innovative source of academic research that discusses the latest approaches to control large-scale systems, and the challenges that occur when implementing them. Highlighting a critical range of topics such as system stability, system stabilization, and fuzzy rules, this book is an ideal publication for engineers, researchers, academics, graduate students, and practitioners interested in the design of large-scale interconnected systems.

Analysis and Design for Positive Stochastic Jump Systems
Analysis and Design for Positive Stochastic Jump Systems

Author: Wenhai Qi

Publisher: Springer Nature

Published: 2022-09-19

Total Pages: 219

ISBN-13: 9811954909

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The book focuses on analysis and design for positive stochastic jump systems. By using multiple linear co-positive Lyapunov function method and linear programming technique, a basic theoretical framework is formed toward the issues of analysis and design for positive stochastic jump systems. This is achieved by providing an in-depth study on several major topics such as stability, time delay, finite-time control, observer design, filter design, and fault detection for positive stochastic jump systems. The comprehensive and systematic treatment of positive systems is one of the major features of the book, which is particularly suited for readers who are interested to learn non-negative theory. By reading this book, the reader can obtain the most advanced analysis and design techniques for positive stochastic jump systems.

Control of Singular Systems with Random Abrupt Changes
Control of Singular Systems with Random Abrupt Changes

Author: El-Kébir Boukas

Publisher: Springer Science & Business Media

Published: 2008-01-12

Total Pages: 268

ISBN-13: 3540743456

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This book deals with the class of singular systems with random abrupt changes also known as singular Markovian jump systems. Various problems and their robustness are tackled. The book examines both the theoretical and practical aspects of the control problems from the angle of the structural properties of linear systems. It can be used as a textbook as well as a reference for researchers in control or mathematics with interest in control theory.