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BL
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| Record Number
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860781
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| Main Entry
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Liu, Xinzhi,1956-
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| Title & Author
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Impulsive systems on hybrid time domains /\ Xinzhi Liu, Kexue Zhang.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2019]
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| Series Statement
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IFSR international series on systems science and engineering ;; volume 33
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| Page. NO
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1 online resource
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| ISBN
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3030062120
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: 3030062139
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: 9783030062125
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: 9783030062132
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3030062112
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9783030062118
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Contents; Part I Introduction; 1 Introduction; 1.1 A Brief History; 1.2 Book Layout; 1.3 Notation; Part II Discrete-Time Impulsive Systems; 2 Stability of Discrete-Time Impulsive Systems with Time-Delay; 2.1 Impulsive Control of Discrete-Time Systems; 2.2 Lyapunov-Razumikhin Technique; 2.2.1 Impulsive Stabilization Results; 2.2.2 Stability Criteria with Arbitrary Impulse Sequences; 2.2.3 Stability Criteria with Impulsive Perturbations; 2.3 The Method of Lyapunov Functionals; 2.3.1 Stability Criteria; 2.3.2 Illustrative Examples
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3 Application to Synchronization of Dynamical Networks3.1 Problem Formulation; 3.2 Synchronization Criteria; 3.3 Numerical Simulations; Part III Continuous-Time Impulsive Systems; 4 Stability of Impulsive Systems with Time-Delay; 4.1 Impulsive Systems with Time-Delay; 4.2 The Method of Lyapunov Functionals; 4.3 Razumikhin Technique; 4.3.1 Results for General Nonlinear Systems; 4.3.2 Case Study: Nonlinear Systems with Distributed-Delay Dependent Impulses; 5 Consensus of Multi-Agent Systems; 5.1 Network Topology; 5.2 Hybrid Protocols with Impulse Delays; 5.2.1 Consensus Protocols
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5.2.2 Some Lemmas5.2.3 Consensus Problem with Fixed Topologies; 5.2.4 Consensus Problem with Switching Topologies; 5.2.5 Discussion and Simulation Results; 5.3 Hybrid Impulsive Protocols with Time-Delay; 5.3.1 Consensus Protocols; 5.3.2 Consensus Results; 5.3.2.1 Networks with Fixed Topologies; 5.3.2.2 Networks with Switching Topologies; 5.3.3 Numerical Simulations; 5.3.4 Proofs; 5.3.4.1 Proof of Theorem 5.3.1; 5.3.4.2 Proof of Theorem 5.3.2; 5.3.4.3 Proof of Theorem 5.3.3; 5.4 Impulsive Protocols with Distributed Delays; 5.4.1 Problem Formulations and Consensus Protocols
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5.4.2 Consensus Results5.4.2.1 Networks with Fixed Topology; 5.4.2.2 Networks with Switching Topologies; 5.4.3 Numerical Simulations; 5.4.4 Proofs; 5.4.4.1 Proof of Theorem 5.4.1; 5.4.4.2 Proof of Theorem 5.4.2; 6 Stabilization and Synchronization of Dynamical Networks; 6.1 Stabilization of Neural Networks with Time-Delay; 6.1.1 Neural Network Model and Preliminaries; 6.1.2 Delay-Dependent Impulsive Control; 6.1.2.1 Numerical Simulations; 6.1.3 Control via Delayed Impulses; 6.1.3.1 Numerical Simulations; 6.2 Synchronization of Nonlinear Time-Delay Systems; 6.2.1 Problem Formulation
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6.2.2 Synchronization Criteria6.2.2.1 Case I: Impulses with Only Discrete Delays (i.e., q1=0 and q2=0); 6.2.2.2 Case II: Impulses with Only Distributed Delays (i.e., q1=0 and q2=0); 6.2.2.3 Case III: Impulses with Both Discrete and Distributed Delays (i.e., q1=0 and q2=0); 6.2.3 Simulation Results; 6.2.4 Proofs; 6.2.4.1 Proof of Theorem 6.2.1; 6.2.4.2 Proof of Theorem 6.2.2; 6.2.4.3 Proof of Theorem 6.2.3; Part IV Impulsive Systems on Time Scales; 7 Differential Equations on Time Scales; 7.1 Introduction of Time Scales; 7.2 Ordinary Differential Equations
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| Abstract
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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.
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| Subject
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Hybrid systems.
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Impulsive differential equations.
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Time delay systems.
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Hybrid systems.
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Impulsive differential equations.
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SCIENCE-- System Theory.
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TECHNOLOGY ENGINEERING-- Operations Research.
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Time delay systems.
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| Dewey Classification
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003
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| LC Classification
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QA76.38
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| Added Entry
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Zhang, Kexue
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