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Internal and External Stabilization of Linear Systems with Constraints

Internal and External Stabilization of Linear Systems with Constraints
Author: Ali Saberi
Publisher: Springer Science & Business Media
Total Pages: 846
Release: 2012-06-21
Genre: Science
ISBN: 0817647872

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Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed. The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.


Stability and Stabilization of Linear Systems with Saturating Actuators

Stability and Stabilization of Linear Systems with Saturating Actuators
Author: Sophie Tarbouriech
Publisher: Springer Science & Business Media
Total Pages: 441
Release: 2011-08-13
Genre: Technology & Engineering
ISBN: 0857299417

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This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.


Stabilization of Linear Systems

Stabilization of Linear Systems
Author: Vasile Dragan
Publisher: Springer Science & Business Media
Total Pages: 326
Release: 1999-06
Genre: Language Arts & Disciplines
ISBN: 9780817639709

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One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability; when the linear approximation is considered, the nat ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic controller. This prob lem was intensively studied during the last decades and many important results have been obtained. The present monograph is based mainly on results obtained by the authors. It focuses on stabilization of systems with slow and fast motions, on stabilization procedures that use only poor information about the system (high-gain stabilization and adaptive stabilization), and also on discrete time implementa tion of the stabilizing procedures. These topics are important in many applications of stabilization theory. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol ogy. This book is not intended to be a text book nor a guide for control-designers. In engineering practice, control-design is a very complex task in which stability is only one of the re quirements and many aspects and facets of the problem have to be taken into consideration. Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo cuses more on the ideas lying behind the recipes. In short, this is not a book on control, but on some mathematics of control.


Stabilization Problems with Constraints

Stabilization Problems with Constraints
Author: Vladimir A Bushenkov
Publisher: CRC Press
Total Pages: 302
Release: 2021-12-17
Genre: Science
ISBN: 1000657469

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Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.


Stabilization Problems with Constraints

Stabilization Problems with Constraints
Author: Vladimir A Bushenkov
Publisher: CRC Press
Total Pages: 306
Release: 1998-04-29
Genre: Science
ISBN: 9789056991418

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Presents and demonstrates stabilizer design techniques that can be used to solve stabilization problems with constraints. These methods have their origins in convex programming and stability theory. However, to provide a practical capability in stabilizer design, the methods are tailored to the special features and needs of this field. Hence, the main emphasis of this book is on the methods of stabilization, rather than optimization and stability theory. The text is divided into three parts. Part I contains some background material. Part II is devoted to behavior of control systems, taking examples from mechanics to illustrate the theory. Finally, Part III deals with nonlocal stabilization problems, including a study of the global stabilization problem.


Topics in Stabilization Under Constraints and Synchronization Problems

Topics in Stabilization Under Constraints and Synchronization Problems
Author: Xu Wang
Publisher:
Total Pages:
Release: 2012
Genre:
ISBN: 9781267671646

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When the issues related to internal stabilization are resolved, the research is directed to simultaneous stabilization problems. The focus here is linear system subject to input saturation. In the case where disturbances that are additive to the input, we complement the existing results in the literature by solving the simultaneous stabilization problems for discrete-time linear systems subject to input saturation. Then attention is paid to non-input-additive disturbances. This research is carried out using a progressive approach. The results are obtained and generalized from a simple double integrator to the most general linear systems. It is found that the simultaneous stabilization problems are solvable if the disturbances do not contained large frequency component corresponding to the open-loop eigenvalues on the stability margin. For those disturbances that meet this criterion, dynamical feedback controller can be constructed to achieve simultaneous stabilization.


Periodic Feedback Stabilization for Linear Periodic Evolution Equations

Periodic Feedback Stabilization for Linear Periodic Evolution Equations
Author: Gengsheng Wang
Publisher: Springer
Total Pages: 135
Release: 2017-02-08
Genre: Science
ISBN: 3319492381

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This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.


Cooperative Control of Multi-agent Systems

Cooperative Control of Multi-agent Systems
Author: Zhenwei Liu
Publisher: Springer Nature
Total Pages: 394
Release: 2022-11-22
Genre: Technology & Engineering
ISBN: 3031129547

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This monograph represents the outcome of research effort of the authors on scalable synchronization of large-scale multi-agent systems (MAS). Cooperative control of multi-agent systems has been growing in popularity and is highly interdisciplinary in recent years. The application of synchronization of MAS includes automobile systems, aerospace systems, multiple-satellite GPS, high-resolution satellite imagery, aircraft formations, highway traffic platooning, industrial process control with multiple processes, and more. Most of the proposed protocols in the literature for synchronization of MAS require some knowledge of the communication network such as bounds on the spectrum of the associated Laplacian matrix and the number of agents. These protocols suffer from scale fragility wherein stability properties are lost for large-scale networks or when the communication graph changes. In the past few years, the authors of this monograph have worked on developing scale-free protocol design for various cases of MAS problems. The key contribution of the monograph is to offer a scale-free design framework and provide scale-free protocols to achieve synchronization, delayed synchronization, and almost synchronization in the presence of input and communication delays, input saturation and external disturbances. The scale-free design framework solely is based on the knowledge of agent models and does not depend on information about the communication network such as the spectrum of the associated Laplacian matrix or size of the network. Drawing upon their extensive work in this area, the authors provide a thorough treatment of agents with higher-order dynamics, different classes of models for agents, and the underlying networks representing actions of the agents. The high technical level of their presentation and their rigorous mathematical approach make this monograph a timely and valuable resource that will fill a gap in the existing literature.