Input To State Stability

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Input-to-State Stability for PDEs

Iasson Karafyllis,Miroslav Krstic
Input to State Stability for PDEs Book PDF

Author : Iasson Karafyllis,Miroslav Krstic
Publisher : Springer
Page : 287 pages
File Size : 47,9 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319910116

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Input-to-State Stability for PDEs by Iasson Karafyllis,Miroslav Krstic Pdf

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Hybrid Dynamical Systems

Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel
Hybrid Dynamical Systems Book PDF

Author : Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel
Publisher : Princeton University Press
Page : 227 pages
File Size : 50,9 Mb
Release : 2012-03-18
Category : Mathematics
ISBN : 9781400842636

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Hybrid Dynamical Systems by Rafal Goebel,Ricardo G. Sanfelice,Andrew R. Teel Pdf

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Mathematical Control Theory

Eduardo D. Sontag
Mathematical Control Theory Book PDF

Author : Eduardo D. Sontag
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 51,8 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461205777

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Mathematical Control Theory by Eduardo D. Sontag Pdf

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Encyclopedia of Systems and Control

John Baillieul,Tariq Samad
Encyclopedia of Systems and Control Book PDF

Author : John Baillieul,Tariq Samad
Publisher : Springer
Page : 1554 pages
File Size : 45,9 Mb
Release : 2015-07-29
Category : Technology & Engineering
ISBN : 1447150570

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Encyclopedia of Systems and Control by John Baillieul,Tariq Samad Pdf

The Encyclopedia of Systems and Control collects a broad range of short expository articles that describe the current state of the art in the central topics of control and systems engineering as well as in many of the related fields in which control is an enabling technology. The editors have assembled the most comprehensive reference possible, and this has been greatly facilitated by the publisher’s commitment continuously to publish updates to the articles as they become available in the future. Although control engineering is now a mature discipline, it remains an area in which there is a great deal of research activity, and as new developments in both theory and applications become available, they will be included in the online version of the encyclopedia. A carefully chosen team of leading authorities in the field has written the well over 250 articles that comprise the work. The topics range from basic principles of feedback in servomechanisms to advanced topics such as the control of Boolean networks and evolutionary game theory. Because the content has been selected to reflect both foundational importance as well as subjects that are of current interest to the research and practitioner communities, a broad readership that includes students, application engineers, and research scientists will find material that is of interest.

Nonlinear and Optimal Control Theory

Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin
Nonlinear and Optimal Control Theory Book PDF

Author : Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin
Publisher : Springer
Page : 360 pages
File Size : 41,7 Mb
Release : 2008-06-24
Category : Science
ISBN : 9783540776536

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Nonlinear and Optimal Control Theory by Andrei A. Agrachev,A. Stephen Morse,Eduardo D. Sontag,Hector J. Sussmann,Vadim I. Utkin Pdf

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

Input-to-State Stability

Andrii Mironchenko
Input to State Stability Book PDF

Author : Andrii Mironchenko
Publisher : Springer Nature
Page : 417 pages
File Size : 44,8 Mb
Release : 2023-03-30
Category : Science
ISBN : 9783031146749

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Input-to-State Stability by Andrii Mironchenko Pdf

Input-to-State Stability presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems. The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs). Features of the book include: • a comprehensive overview of the theoretical basis of ISS; • a description of the central applications of ISS in nonlinear control theory; • a detailed discussion of the role of small-gain methods in the stability of nonlinear networks; and • an in-depth comparison of ISS for finite- and infinite-dimensional systems. The book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS. The reader should have a basic knowledge of analysis, Lebesgue integration theory, linear algebra, and the theory of ODEs but requires no prior knowledge of dynamical systems or stability theory. The author introduces all the necessary ideas within the book. Input-to-State Stability will interest researchers and graduate students studying nonlinear control from either a mathematical or engineering background. It is intended for active readers and contains numerous exercises of varying difficulty, which are integral to the text, complementing and widening the material developed in the monograph.

Nonlinear Dynamical Systems and Control

Wassim M. Haddad,VijaySekhar Chellaboina
Nonlinear Dynamical Systems and Control Book PDF

Author : Wassim M. Haddad,VijaySekhar Chellaboina
Publisher : Princeton University Press
Page : 975 pages
File Size : 53,7 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9781400841042

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Nonlinear Dynamical Systems and Control by Wassim M. Haddad,VijaySekhar Chellaboina Pdf

Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Stabilization of Linear Systems

Vasile Dragan,Aristide Halanay
Stabilization of Linear Systems Book PDF

Author : Vasile Dragan,Aristide Halanay
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 49,6 Mb
Release : 1999-06
Category : Language Arts & Disciplines
ISBN : 0817639705

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Stabilization of Linear Systems by Vasile Dragan,Aristide Halanay Pdf

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.

Nonlinear Control Under Nonconstant Delays

Nikolaos Bekiaris-Liberis,Miroslav Krstic
Nonlinear Control Under Nonconstant Delays Book PDF

Author : Nikolaos Bekiaris-Liberis,Miroslav Krstic
Publisher : SIAM
Page : 293 pages
File Size : 48,8 Mb
Release : 2013-09-25
Category : Mathematics
ISBN : 9781611973174

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Nonlinear Control Under Nonconstant Delays by Nikolaos Bekiaris-Liberis,Miroslav Krstic Pdf

The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept?with constant delays only on the input?all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.

Stability and Stabilization of Nonlinear Systems

Iasson Karafyllis,Zhong-Ping Jiang
Stability and Stabilization of Nonlinear Systems Book PDF

Author : Iasson Karafyllis,Zhong-Ping Jiang
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 48,9 Mb
Release : 2011-04-02
Category : Technology & Engineering
ISBN : 9780857295132

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Stability and Stabilization of Nonlinear Systems by Iasson Karafyllis,Zhong-Ping Jiang Pdf

Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of their stability and feedback stabilization which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Stability and Stabilization

William J. Terrell
Stability and Stabilization Book PDF

Author : William J. Terrell
Publisher : Princeton University Press
Page : 484 pages
File Size : 55,7 Mb
Release : 2009-02-15
Category : Mathematics
ISBN : 0691134448

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Stability and Stabilization by William J. Terrell Pdf

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Designed for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, the book takes a unique modern approach that bridges the gap between linear and nonlinear systems. Presenting stability and stabilization of equilibria as a core problem of mathematical control theory, the book emphasizes the subject's mathematical coherence and unity, and it introduces and develops many of the core concepts of systems and control theory. There are five chapters on linear systems and nine chapters on nonlinear systems; an introductory chapter; a mathematical background chapter; a short final chapter on further reading; and appendixes on basic analysis, ordinary differential equations, manifolds and the Frobenius theorem, and comparison functions and their use in differential equations. The introduction to linear system theory presents the full framework of basic state-space theory, providing just enough detail to prepare students for the material on nonlinear systems. Focuses on stability and feedback stabilization Bridges the gap between linear and nonlinear systems for advanced undergraduates and beginning graduate students Balances coverage of linear and nonlinear systems Covers cascade systems Includes many examples and exercises

Finite-Time Stability: An Input-Output Approach

Francesco Amato,Gianmaria De Tommasi,Alfredo Pironti
Finite Time Stability An Input Output Approach Book PDF

Author : Francesco Amato,Gianmaria De Tommasi,Alfredo Pironti
Publisher : John Wiley & Sons
Page : 184 pages
File Size : 47,9 Mb
Release : 2018-10-08
Category : Technology & Engineering
ISBN : 9781119140528

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Finite-Time Stability: An Input-Output Approach by Francesco Amato,Gianmaria De Tommasi,Alfredo Pironti Pdf

Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.

Stochastic Differential Equations with Markovian Switching

Xuerong Mao,Chenggui Yuan
Stochastic Differential Equations with Markovian Switching Book PDF

Author : Xuerong Mao,Chenggui Yuan
Publisher : Imperial College Press
Page : 430 pages
File Size : 43,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9781860947018

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Stochastic Differential Equations with Markovian Switching by Xuerong Mao,Chenggui Yuan Pdf

This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.

Switching in Systems and Control

Daniel Liberzon
Switching in Systems and Control Book PDF

Author : Daniel Liberzon
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461200178

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Switching in Systems and Control by Daniel Liberzon Pdf

The theory of switched systems is related to the study of hybrid systems, which has gained attention from control theorists, computer scientists, and practicing engineers. This book examines switched systems from a control-theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. It includes a vast bibliography and a section of technical and historical notes.

Nonlinear Systems Analysis

M. Vidyasagar
Nonlinear Systems Analysis Book PDF

Author : M. Vidyasagar
Publisher : SIAM
Page : 515 pages
File Size : 45,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0898719186

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Nonlinear Systems Analysis by M. Vidyasagar Pdf

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.