Methogologies for Control of Jump Time-delay Systems

Methogologies for Control of Jump Time-delay Systems

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English

Description

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 Markov random process. This book is about the time-domain modeling, stability, stabilization, control design and filtering for JTDS. It gives readers a thorough understanding of the basic mathematical analysis and fundamentals of JTDS. Additionally, it offers a straightforward treatment of the different topics and provides a broad coverage of the recent methodologies. The prime concern has been on the interplay between delay factors, jumping behavior and parametric uncertainties. The cases of single and interconnected JTDS are considered and numerous examples are worked out. The relationship to previous results on time-delay systems (TDS) and Markovian jump systems (MJS) are revealed. The book is a good volume for independent study or a reference for practicing engineers, interested readers, researchers and students.

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Published 21 January 2013
Reads 3
EAN13 0306487233
License: All rights reserved
Language English

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Contents
1Introduction 1.1Overview 1.2Historical Perspectives 1.3A Glossary of Terminology and Notations 1.3.1 General Terms 1.3.2 Functional Differential Equations 1.3.3 Markov Processes 1.4Main Features of the Book 1.5Notes and References
2Jump TimeDelay Systems 2.1Examples of TimeDelay Systems 2.1.1 Economic Systems 2.1.2Nuclear Reactors 2.1.3PredatorPrey Models 2.2Examples of Jump Systems 2.2.1Manufacturing Flow Control 2.2.2Optimal Inventory/Production Control 2.3Classes of Jump TimeDelay Systems
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15 15 16 18 18 20 21 24 25
27 27 27 29 30 30 30 31 33
2.4
2.3.1Model of Uncertainties Relevant Special Cases 2.4.1Nominal Models 2.4.2Uncertain Models
3Stochastic Stability and Stabilization 3.1Introduction 3.2ModeIndependent Stochastic Stability 3.2.1Weak DelayDependence 3.2.2Strong DelayDependence 3.2.3Examples 3.3ModeDependent Stochastic Stability 3.3.1ModeDependent Model 3.3.2WeakDelay Dependence 3.3.3Strong DelayDependence 3.3.4Example 3.3 3.4Robust Stabilization 3.4.1ModeIndependent Results 3.4.2ModeDependent Results 3.4.3Memoryless Feedback 3.4.4Delayed Feedback 3.4.5Example 3.4 3.5Notes and References
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Control System Design 4.1Introduction 4.2Problem Description 4.3Control Objective
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35 37 37 39
43 43 45 46 53 62 67 68 70 77 85 87 87 91 92 94 97 98
101 101 102 103
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4.4Robust Performance Analysis 4.4.1 Weak Delay Dependence 4.4.2Strong DelayDependence 4.5Guaranteed Cost Control 4.5.1WeakDelay Dependence 4.5.2Special Cases 4.5.3 Strong Delay Dependence 4.6Feedback 4.7Numerical Examples 4.7.1 Example 4.1 4.7.2Example 4.2 4.7.3 Example 4.3 4.8Feedback 4.8.1 Weak DelayDependence 4.8.2Strong DelayDependence 4.8.3 Example 4.4 4.9Transformation Method 4.9.1 Problem Description 4.9.2Model Transformation 4.9.3 Example 4.5 4.10 Notes and References
Simultaneous Control 5.1Introduction 5.2Problem Statement 5.3Direct Approach 5.3.1 ModeDependent Nominal Model 5.3.2 Performance
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104 105 111 115 116 120 122 130 137 137 139 140 141 141 148 154 157 157 160 170 171
173 173 174 176 177 178
5.4
5.5
5.6
5.7 5.8
5.3.3Performance 5.3.4Mixed Performance 5.3.5Example 5.1 5.3.6Uncertain Model Design 5.3.7 5.3.8 5.3.9Mixed Performance 5.3.10Example 5.2 5.3.11Extensions State Transformation Approach 5.4.1State Transformation 5.4.2Nominal Design 5.4.3 5.4.4Performance 5.4.5MixedControl 5.4.6Design with Uncertainties 5.4.7Performance 5.4.8Performance 5.4.9Mixed Performance Examples 5.5.1Example 5.3 5.5.2Example 5.4 Descriptor Approach 5.6.1Descriptor Transformation 5.6.2Simultaneous Nominal Design Simultaneous Uncertain Design Examples
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185 188 189 191 192 195 197 197 198 200 201 202 203 210 213 214 216 219 221 221 221 224 225 225 226 238 244
5.9
5.8.1 Example 5.5 5.8.2Example 5.6 Notes and References
6Robust Filtering 6.1Introduction 6.2System Description 6.3Robust Kalman Filtering 6.3.1 Preliminary Results 6.3.2Robust Filter 6.3.3Robust SteadyState Filter 6.3.4Example 6.1 6.4RobustFiltering 6.4.1 Problem Formulation 6.4.2Preliminary Results 6.4.3 Linear Filtering 6.4.4Augmented System 6.4.5Design Procedure 6.4.6Example 6.2 6.5Filtering with Modedependent Delays 6.5.1 Problem Formulation 6.5.2Linear Markovian Filter 6.5.3 State Error Dynamics 6.5.4Filtering 6.5.5 Example 6.3 6.6Notes and References
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245 247 248
249 249 250 252
252 256 260 265 267 268 270 272 273 274 278
279 280 283 283 292 295 297
7Neutral Jumping Systems 7.1Introduction 7.2Model Description 7.2.1Stability Analysis 7.3Robust Stabilization 7.3.1Memoryless Feedback 7.3.2Distributed Feedback 7.4Feedback 7.4.1The ClosedLoop System 7.4.2Example 7.1 7.5Robust Observers 7.5.1Structure of Observer 7.5.2Design Procedure 7.5.3Performance 7.5.4Robust Stabilization 7.6Examples 7.6.1Example 7.2 7.6.2Example 7.3 7.7Notes and References
8Interconnected Systems 8.1Introduction 8.2Problem Statement 8.3Nominal Analysis and Design 8.3.1Stability Results 8.3.2Stabilization Results 8.3.3Feedback Control 8.4Robust Analysis and Design
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299 299 301 305 316 316 321 326 326 335 337 340 345 350 356 363 364 365 366
369 369 370 375 375 380 382 391
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8.5
8.6 8.7 8.8
8.4.1Robust Analysis 8.4.2Robust Design 8.4.3Uncertain Jumping Rates Robust Decentralized Dynamic Feedback 8.5.1Algorithm Decentralized Robust Performance Example 8.1 Notes and References
Appendix 9.1Standard Facts 9.2Some Common Lyapunov Functionals
10Bibliography
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391 393 397 400 411 414 423 427
429 429 434
437