Methodologies for Control of Jump Time-Delay Systems
Jump Time-Delay Systems (JTDS) represent a new class of piece-wise deterministic systems, in which the underlying dynamics is governed by delay-differential equations and it possesses multiple modes of operation depending on the value of an associated Mar
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Methodologies for Control of Jump Time-Delay Systems by
Magdi S. Mahmoud Faculty of Engineering, Arab Academy for Sciences & Technology, Egypt and
Peng Shi Weapons Systems Division, Defense and Technology Organization, Australia
KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: Print ISBN:
0-306-48723-3 1-4020-7489-1
©2004 Springer Science + Business Media, Inc. Print ©2003 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America
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To The Memory of my Parents and To My Family (Salwa, Medhat, Monda, Mohamed) MSM To The Memory of my Father and To My Family (Fengmei, Lisa, Michael) PS
Contents 1 Introduction
15
1.1 Overview
15
1.2 Historical Perspectives
16
1.3 A Glossary of Terminology and Notations
18
1.3.1
General Terms
18
1.3.2
Functional Differential Equations
20
1.3.3
Markov Processes
21
1.4 Main Features of the Book
24
1.5 Notes and References
25
2 Jump Time-Delay Systems
27
2.1 Examples of Time-Delay Systems
2.2
27
2.1.1
Economic Systems
27
2.1.2
Nuclear Reactors
29
2.1.3
Predator-Prey Models
30
Examples of Jump Systems
30
2.2.1
Manufacturing Flow Control
30
2.2.2
Optimal Inventory/Production Control
31
2.3 Classes of Jump Time-Delay Systems
1
33
2.3.1
Model of Uncertainties
2.4 Relevant Special Cases
37
2.4.1
Nominal Models
37
2.4.2
Uncertain Models
39
3 Stochastic Stability and Stabilization
3.1 Introduction 3.2
35
43
43
Mode-Independent Stochastic Stability
45
3.2.1
Weak Delay-Dependence
46
3.2.2
Strong Delay-Dependence
53
3.2.3
Examples
62
3.3 Mode-Dependent Stochastic Stability
67
3.3.1
Mode-Dependent Model
68
3.3.2
Weak-Delay Dependence
70
3.3.3
Strong Delay-Dependence
77
3.3.4
Example 3.3
85
3.4 Robust Stabilization
87
3.4.1
Mode-Independent Results
87
3.4.2
Mode-Dependent Results
91
3.4.3
Memoryless Feedback
92
3.4.4
Delayed Feedback
94
3.4.5
Example 3.4
97
3.5 Notes and References
98
4 Control System Design
101
4.1 Introduction 4.2
101
Problem Description
102
4.3 Control Objective
103
2
104
4.4 Robust Performance Analysis
4.5
4.4.1
Weak Delay Dependence
105
4.4.2
Strong Delay-Dependence
111
Guaranteed Cost Control
115
4.5.1
Weak-Delay Dependence
116
4.5.2
Special Cases
120
4.5.3
Strong Delay Dependence
122 130
Feedback
4.6
4.7 Numerical Examples
137
4.7.1
Example 4.1
137
4.7.2
Example 4.2
139
4.7.3
Example 4.3
140 141
Feedback
4.8
4.8.1
Weak Delay-Dependence
141
4.8.2
Strong Delay-Dependence
148
4.8.3
Example 4.4
154
4.9 Transformation Method
157
4.9.1
Problem Description
157
4.9.2
Model Transformation
160
4.9.3
Example 4.5
170
4.10 Notes a
