Download or read book Stability and Boundedness of Impulsive Systems with Time Delay written by Qing Wang and published by . This book was released on 2007 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability and boundedness theories are developed for impulsive differential equations with time delay. Definitions, notations and fundamental theory are presented for delay differential systems with both fixed and state-dependent impulses. It is usually more difficult to investigate the qualitative properties of systems with state-dependent impulses since different solutions have different moments of impulses. In this thesis, the stability problems of nontrivial solutions of systems with state-dependent impulses are ``transferred" to those of the trivial solution of systems with fixed impulses by constructing the so-called ``reduced system". Therefore, it is enough to investigate the stability problems of systems with fixed impulses. The exponential stability problem is then discussed for the system with fixed impulses. A variety of stability criteria are obtained and`numerical examples are worked out to illustrate the results, which shows that impulses do contribute to the stabilization of some delay differential equations. To unify various stability concepts and to offer a general framework for the investigation of stability theory, the concept of stability in terms of two measures is introduced and then several stability criteria are developed for impulsive delay differential equations by both the single and multiple Lyapunov functions method. Furthermore, boundedness and periodicity results are discussed for impulsive differential systems with time delay. The Lyapunov-Razumikhin technique, the Lyapunov functional method, differential inequalities, the method of variation of parameters, and the partitioned matrix method are the main tools to obtain these results. Finally, the application of the stability theory to neural networks is presented. In applications, the impulses are considered as either means of impulsive control or perturbations. Sufficient conditions for stability and stabilization of neural networks are obtained.
Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009-10-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Download or read book Impulsive Systems with Delays written by Xiaodi Li and published by Springer Nature. This book was released on 2021-10-15 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically presents the most recent progress in stability and control of impulsive systems with delays. Impulsive systems have recently attracted continued high research interests because they provide a natural framework for mathematical modeling of many real-world processes. It focuses not only on impulsive delayed systems, but also impulsive systems with delayed impulses and impulsive systems with event-triggered mechanism, including their Lyapunov stability, finite-time stability and input-to-state stability synthesis. Special attention is paid to the bilateral effects of the delayed impulses, where comprehensive stability properties are discussed in the framework of time-dependent and state-dependent delays. New original work with event-triggered impulsive control and its applications in multi-agent systems and collective dynamics are also provided. This book will be of use to specialists who are interested in the theory of impulsive differential equations and impulsive control theory, as well as high technology specialists who work in the fields of complex networks and applied mathematics. Also, instructors teaching graduate courses and graduate students will find this book a valuable source of nonlinear system theory.
Download or read book Finite Time Stability An Input Output Approach written by Francesco Amato and published by John Wiley & Sons. This book was released on 2018-10-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boundedness and Stability Properties of Impulsive Systems written by George Henri Ballinger and published by . This book was released on 1995 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Impulsive Differential Equations written by Drumi Bainov and published by Routledge. This book was released on 2017-11-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.
Download or read book Advances in Time Delay Systems written by Silviu-Iulian Niculescu and published by Springer Science & Business Media. This book was released on 2004-04-21 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on delay systems and their applications. Well-known experts in the field were brought together to present a wide panorama of interdisciplinary methods in handling stability, control and related numerical issues. By reading the book, the readers will get an up-to-date picture of this active area of research as well as representative methods used in this field. This book can be used as a reference for both experts and novices interested in the research of time-delay, numerical issues, as well as applications of time-delay systems.
Download or read book Systems with Impulse Effect written by Dimitŭr Baĭnov and published by . This book was released on 1989 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of Time Delay Systems written by Keqin Gu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.
Download or read book Impulsive Differential Equations written by N Perestyuk and published by World Scientific. This book was released on 1995-08-31 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts
Download or read book Impulsive Systems on Hybrid Time Domains written by Xinzhi Liu and published by Springer. This book was released on 2019-01-29 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses the issues of stability and the control of impulsive systems on hybrid time domains, with systems presented on discrete-time domains, continuous-time domains, and hybrid-time domains (time scales). Research on impulsive systems has recently attracted increased interest around the globe, and significant progress has been made in the theory and application of these systems. This book introduces recent developments in impulsive systems and fundamentals of various types of differential and difference equations. It also covers studies in stability related to time delays and other various control applications on the different impulsive systems. In addition to the analyses presented on dynamical systems that are with or without delays or impulses, this book concludes with possible future directions pertaining to this research.
Download or read book Almost Periodic Solutions of Impulsive Differential Equations written by Gani T. Stamov and published by Springer Science & Business Media. This book was released on 2012-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.
Download or read book Truncated Predictor Feedback for Time Delay Systems written by Bin Zhou and published by Springer. This book was released on 2014-05-29 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic approach to the design of predictor based controllers for (time-varying) linear systems with either (time-varying) input or state delays. Differently from those traditional predictor based controllers, which are infinite-dimensional static feedback laws and may cause difficulties in their practical implementation, this book develops a truncated predictor feedback (TPF) which involves only finite dimensional static state feedback. Features and topics: A novel approach referred to as truncated predictor feedback for the stabilization of (time-varying) time-delay systems in both the continuous-time setting and the discrete-time setting is built systematically Semi-global and global stabilization problems of linear time-delay systems subject to either magnitude saturation or energy constraints are solved in a systematic manner Both stabilization of a single system and consensus of a group of systems (multi-agent systems) are treated in a unified manner by applying the truncated predictor feedback and predictor feedback The properties of the solutions to a class of parametric (differential and difference) Lyapunov matrix equations are presented in detail Detailed numerical examples and applications to the spacecraft rendezvous and formation flying problems are provided to demonstrate the usefulness of the presented theoretical results This book can be a useful resource for the researchers, engineers, and graduate students in the fields of control, applied mathematics, mechanical engineering, electrical engineering, and aerospace engineering.
Download or read book Qualitative Analysis of Set Valued Differential Equations written by Anatoly A. Martynyuk and published by Springer. This book was released on 2019-04-02 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.
Download or read book Functional and Impulsive Differential Equations of Fractional Order written by Ivanka Stamova and published by CRC Press. This book was released on 2017-03-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.
Download or read book Stability and Stabilization of Time Delay Systems written by Wim Michiels and published by SIAM. This book was released on 2007-01-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems.
Download or read book Dynamics and Stability of Motion of Shock and Hybrid Systems written by Anatoliy A. Martynyuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-04-15 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Buy this book on degruyter.com“A href="https://www.degruyter.com/viewbooktoc/product/538686">https://www.degruyter.com/viewbooktoc/product/538686
