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E-raamat: Impulsive Systems on Hybrid Time Domains

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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.

Arvustused

The book can be used as a reference for graduate students as well as active researchers. (Mehdi Nategh, Mathematical Reviews, August, 2019)

Part I Introduction
1 Introduction
3(8)
1.1 A Brief History
3(2)
1.2 Book Layout
5(2)
1.3 Notation
7(4)
Part II Discrete-Time Impulsive Systems
2 Stability of Discrete-Time Impulsive Systems with Time-Delay
11(50)
2.1 Impulsive Control of Discrete-Time Systems
11(4)
2.2 Lyapunov-Razumikhin Technique
15(29)
2.2.1 Impulsive Stabilization Results
15(7)
2.2.2 Stability Criteria with Arbitrary Impulse Sequences
22(14)
2.2.3 Stability Criteria with Impulsive Perturbations
36(8)
2.3 The Method of Lyapunov Functionals
44(17)
2.3.1 Stability Criteria
44(9)
2.3.2 Illustrative Examples
53(8)
3 Application to Synchronization of Dynamical Networks
61(12)
3.1 Problem Formulation
61(2)
3.2 Synchronization Criteria
63(3)
3.3 Numerical Simulations
66(7)
Part III Continuous-Time Impulsive Systems
4 Stability of Impulsive Systems with Time-Delay
73(24)
4.1 Impulsive Systems with Time-Delay
73(5)
4.2 The Method of Lyapunov Functionals
78(7)
4.3 Razumikhin Technique
85(12)
4.3.1 Results for General Nonlinear Systems
85(2)
4.3.2 Case Study: Nonlinear Systems with Distributed-Delay Dependent Impulses
87(10)
5 Consensus of Multi-Agent Systems
97(44)
5.1 Network Topology
98(1)
5.2 Hybrid Protocols with Impulse Delays
98(11)
5.2.1 Consensus Protocols
99(1)
5.2.2 Some Lemmas
100(1)
5.2.3 Consensus Problem with Fixed Topologies
101(2)
5.2.4 Consensus Problem with Switching Topologies
103(2)
5.2.5 Discussion and Simulation Results
105(4)
5.3 Hybrid Impulsive Protocols with Time-Delay
109(14)
5.3.1 Consensus Protocols
109(1)
5.3.2 Consensus Results
110(5)
5.3.3 Numerical Simulations
115(4)
5.3.4 Proofs
119(4)
5.4 Impulsive Protocols with Distributed Delays
123(18)
5.4.1 Problem Formulations and Consensus Protocols
123(3)
5.4.2 Consensus Results
126(3)
5.4.3 Numerical Simulations
129(2)
5.4.4 Proofs
131(10)
6 Stabilization and Synchronization of Dynamical Networks
141(40)
6.1 Stabilization of Neural Networks with Time-Delay
141(20)
6.1.1 Neural Network Model and Preliminaries
142(2)
6.1.2 Delay-Dependent Impulsive Control
144(5)
6.1.3 Control via Delayed Impulses
149(12)
6.2 Synchronization of Nonlinear Time-Delay Systems
161(20)
6.2.1 Problem Formulation
161(1)
6.2.2 Synchronization Criteria
162(2)
6.2.3 Simulation Results
164(5)
6.2.4 Proofs
169(12)
Part IV Impulsive Systems on Time Scales
7 Differential Equations on Time Scales
181(32)
7.1 Introduction of Time Scales
181(4)
7.2 Ordinary Differential Equations
185(1)
7.3 Functional Differential Equations
186(27)
7.3.1 Problem Formulation
186(4)
7.3.2 Basic Theory
190(4)
7.3.3 Uniform Stability Results
194(6)
7.3.4 Exponential Stability Results
200(9)
7.3.5 Numerical Examples
209(4)
8 Stability in Terms of Two Measures of Impulsive Systems on Time Scales
213(48)
8.1 Introduction and Problem Formulation
213(2)
8.2 Comparison Method
215(26)
8.2.1 Comparison Result
216(2)
8.2.2 Comparison Stability Theorems
218(12)
8.2.3 Applications to Impulsive Control of Chaotic Systems
230(11)
8.3 Lyapunov Direct Method
241(20)
8.3.1 (h0, h)-(Uniform) Stability
242(5)
8.3.2 {h0, h)-(Uniform) Asymptotic Stability
247(7)
8.3.3 (h0, h)-Instability
254(3)
8.3.4 Examples
257(4)
9 Exponential Stability of Impulsive Time-Delay Systems on Time Scales
261(24)
9.1 Problem Formulation
261(2)
9.2 Razumikhin Type Theorems
263(11)
9.3 The Method of Lyapunov Functionals
274(11)
10 Control Problems on Time Scales
285(20)
10.1 Controllability and Observability of Impulsive Time-Varying Linear Systems on Time Scales
285(6)
10.1.1 Problem Formulation
286(1)
10.1.2 Controllability
287(1)
10.1.3 Observability
288(2)
10.1.4 Summaries
290(1)
10.2 Synchronization of Linear Dynamical Networks on Time Scales
291(14)
10.2.1 Problem Formulation
291(2)
10.2.2 Synchronization Results
293(5)
10.2.3 Numerical Simulations
298(7)
Part V Conclusions and Future Work
11 Conclusions and Future Directions
305(4)
11.1 Stability Analysis
305(1)
11.2 Impulsive Consensus
306(1)
11.3 Pinning Impulsive Control
307(1)
11.4 Control Problems on Time Scales
308(1)
References 309(8)
Index 317
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