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E-raamat: Theory of Hybrid Systems: Deterministic and Stochastic

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  • Formaat: EPUB+DRM
  • Sari: Nonlinear Physical Science
  • Ilmumisaeg: 04-Oct-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811080463
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Theory of Hybrid Systems: Deterministic and StochasticSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Nonlinear Physical Science
  • Ilmumisaeg: 04-Oct-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811080463
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This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin–Lyapunov methods to investigate the systems’ properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.

1 Motivating Examples
1(4)
1.1 Switched Systems
1(2)
1.1.1 Supervisory Switching Control
1(1)
1.1.2 Switched Server System
2(1)
1.1.3 Singular System with Markov Switching
2(1)
1.2 Impulsive Systems
3(1)
1.2.1 SEIRS Epidemic Model with Impulse Vaccinations
3(1)
1.2.2 Insulin Treatment
4(1)
References
4(1)
2 Mathematical Background
5(54)
2.1 Basic Definitions
5(5)
2.2 Comparison Method
10(2)
2.3 Delay Systems
12(3)
2.4 Impulsive Systems
15(5)
2.5 Comparison Method for Impulsive Systems
20(2)
2.6 Impulsive Systems with Time Delay
22(2)
2.7 Stochastic Differential Equations
24(12)
2.7.1 Notations and Basic Definitions
24(3)
2.7.2 Stochastic Processes
27(2)
2.7.3 Stochastic Differential Equations
29(6)
2.7.4 Comparison Method for Stochastic Systems
35(1)
2.8 Stochastic Impulsive System with Time Delay
36(2)
2.9 Switched Systems
38(6)
2.9.1 System Formulation
38(3)
2.9.2 Systems with Stable Subsystems
41(3)
2.10 Stochastic Switched Systems with Time Delay
44(5)
2.11 Singularly Perturbed Systems
49(3)
2.12 Miscellaneous Results
52(2)
2.13 Notes and Comments
54(1)
References
55(4)
3 Fundamental Properties of Stochastic Impulsive Systems with Time Delay
59(18)
3.1 Existence of Solution
61(8)
3.2 Forward Continuation
69(3)
3.3 Global Existence
72(1)
3.4 Uniqueness of Solution
73(1)
3.5 Notes and Comments
74(1)
References
75(2)
4 Stability of Stochastic Impulsive Systems with Time Delay
77(20)
4.1 Stability Analysis by Classical Lyapunov Technique
78(7)
4.2 Stability Analysis by Comparison Method
85(10)
4.3 Notes and Comments
95(1)
References
95(2)
5 Large-Scale Stochastic Impulsive Systems with Time Delay
97(20)
5.1 Problem Formulation
97(4)
5.2 Analysis by Lyapunov Method
101(4)
5.3 Comparison Method
105(6)
5.3.1 Method of Lyapunov Function
105(2)
5.3.2 Method of Vector Lyapunov Functions
107(4)
5.4 Examples
111(5)
5.5 Notes and Comments
116(1)
References
116(1)
6 Input-to-State Stability for Stochastic Switched Systems
117(18)
6.1 Problem Formulation
117(4)
6.2 Initial-State-Dependent Dwell-Time
121(7)
6.3 Markovian Switching
128(5)
6.4 Notes and Comments
133(1)
References
134(1)
7 Reliable Control for Stochastic Switched Systems with State Delay
135(10)
7.1 Problem Formulation
135(2)
7.2 Stability Analysis
137(3)
7.3 Numerical Example
140(2)
7.4 Notes and Comments
142(1)
References
142(3)
8 Robust Reliable Control for Impulsive Large-Scale Systems
145(20)
8.1 Problem Formulation
145(2)
8.2 Reliable Control
147(9)
8.3 State Estimation
156(7)
8.4 Notes and Comments
163(1)
References
163(2)
9 Switched Singularly Perturbed Systems with Time Delay
165(12)
9.1 Problem Formulation
165(1)
9.2 Stability Analysis
166(9)
9.2.1 Linear Systems
166(5)
9.2.2 Nonlinear Systems
171(4)
9.3 Notes and Comments
175(1)
References
175(2)
10 Singularly Perturbed Impulsive-Switched Systems with Time Delay
177(14)
10.1 Problem Formulation
177(1)
10.2 Stability Analysis
178(12)
10.2.1 Linear Systems
178(8)
10.2.2 Nonlinear Systems
186(4)
10.3 Notes and Comments
190(1)
Reference
190(1)
11 Stabilization and State Estimation via Sliding Mode Control
191(16)
11.1 Problem Formulation
191(1)
11.2 Slow Sliding Mode Control Design
192(6)
11.2.1 Sliding Mode Control with Multiple Inputs
193(1)
11.2.2 Reachability Analysis
194(4)
11.3 Sliding Mode Luenberger Observer
198(4)
11.4 Numerical Examples
202(3)
11.5 Notes and Comments
205(1)
References
206(1)
12 Comparison Method and Stability of EPCA
207(22)
12.1 Introduction
207(1)
12.2 Problem Formulation
208(2)
12.3 Comparison Method
210(6)
12.4 Stability Analysis
216(6)
12.5 Numerical Examples
222(3)
12.6 Application
225(1)
12.7 Notes and Comments
226(1)
References
227(2)
13 Existence, Uniqueness and Stability of Stochastic EPCA
229
13.1 Existence and Uniqueness of Solutions
230(6)
13.2 Comparison Method
236(2)
13.3 Stability Analysis
238(3)
13.4 Notes and Comments
241(1)
References
241
Dr. Mohamad S. Alwan is a lecturer at the Department of Applied Mathematics at the University of Waterloo. Since 2004, his research interests have been directed towards broadening the research area of Stochastic and Deterministic Hybrid Systems with/without Time Delay and Applications to Control Systems. Specifically, he has been working on establishing many system properties and applying some of these properties to control systems. He has published several peer-reviewed journal papers, conference papers, and book chapters, most of which are included in the book.

Professor Xinzhi Liu is a faculty member of the Department of Applied Mathematics at the University of Waterloo. He received his Ph.D. degree in Applied Mathematics from the University of Texas at Arlington. He is an expert on hybrid dynamical systems, stability theory and control methods. He has been the editor-in- chief of the Journal--Dynamics of Continuous, Discrete and Impulsive Systems since 1995. He has published over 300 research papers and 3 monographs and 20 edited books on different topics in the field of dynamical systems.





 
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