Lecture Notes in Control and Information Sciences

By: Yuanqing Xia, Mengyin Fu, Peng Shi

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Paperback | 7 September 2009

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Time-delay occurs in many dynamical systems such as biological systems, chemical systems, metallurgical processing systems, nuclear reactor, long transmission lines in pneumatic, hydraulic systems and electrical networks. Especially, in recent years, time-delay which exists in networked control systems has brought more complex problem into a new research area. Frequently, it is a source of the generation of oscillation, instability and poor performance. Considerable effort has been applied to different aspects of linear time-delay systems during recent years. Because the introduction of the delay factor renders the system analysis more complicated, in addition to the difficulties caused by the perturbation or uncertainties, in the control of time-delay systems, the problems of robust stability and robust stabilization are of great importance.

This book presents some basic theories of stability and stabilization of systems with time-delay, which are related to the main results in this book. More attention will be paid on synthesis of systems with time-delay. That is, sliding mode control of systems with time-delay, networked control systems with time-delay, networked data fusion with random delay.

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Basic Theory for Systems with Time-Delay
Recent Results on Analysis of Systems with Time-Delay	p. 3
Introduction	p. 3
Problem Formulation	p. 4
Delay-Independent Conditions	p. 5
Delay-Dependent Conditions	p. 5
Basic Approaches	p. 6
Recent Results on Interval Time-Varying Delay System	p. 12
Conclusion	p. 16
New Results on Stability of Systems With Interval Time-Varying Delay	p. 17
Introduction	p. 17
Problem Formulation	p. 18
Main Results	p. 18
Numerical Example	p. 21
Conclusion	p. 23
Stability and Stabilization for Discrete Systems with Time-Delay	p. 25
Introduction	p. 25
Problem Formulation	p. 26
Main Results	p. 26
Stability analysis	p. 26
Controller Design	p. 29
Numerical Example	p. 34
Conclusion	p. 34
Sliding Mode Control (SMC) for Systems with Time-Delay
Robust SMC for Uncertain Time-Delay Systems	p. 37
Introduction	p. 37
Problem Formulation	p. 38
Main Results	p. 41
Numerical Example	p. 46
Conclusion	p. 48
Robust Delay-Dependent SMC for Uncertain Time-Delay Systems	p. 49
Introduction	p. 49
Problem Formulation	p. 50
Main Results	p. 52
Design of Linear Sliding Surface	p. 53
Design of A Reaching Motion Controller	p. 60
Numerical Example	p. 62
Conclusion	p. 64
Robust Adaptive SMC for Uncertain Time-Delay Systems	p. 67
Introduction	p. 67
Problem Formulation	p. 67
Main Results	p. 70
Numerical Example	p. 79
Conclusion	p. 83
SMC of Uncertain Linear Discrete Time Systems with Input Delay	p. 85
Problem Formulation	p. 86
Predictor-Based SMC	p. 87
Predictor in Discrete-Time	p. 87
Predictor-Based SMC for System S_1	p. 89
Robust Predictor Based SMC for System S_2	p. 90
Stability Analysis of Quasi-Sliding Motion	p. 91
Numerical Example	p. 95
Conclusion	p. 97
SMC for Linear Systems with Input and State Delays	p. 99
Introduction	p. 99
Problem Formulation	p. 100
Compensator-Based SMC for Systems with Time Delay	p. 100
SMC for Linear Systems with Time-varying Input and State Delays	p. 108
Compensator-Based SMC for Systems with Time-varying Delays	p. 108
Numerical Example	p. 113
Conclusion	p. 117
Robust SMC for Uncertain Time-Delay Systems Based on Delta Operator	p. 119
Introduction	p. 119
Problem Formulation	p. 121
Main Results	p. 124
Numerical Example	p. 131
Conclusion	p. 135
ADRC for Uncertain Systems with Time-Delay	p. 137
Introduction	p. 137
Problem Formulation	p. 138
Concepts of TD, ESO and Nonlinear Feedback Controller	p. 143
Example	p. 146
Conclusion	p. 149
Networked Control Systems (NCSs) with Random Time-Delay
Analysis and Synthesis of NCSs with Random Forward Delay	p. 153
Introduction	p. 153
Networked Predictive Control for Systems with Networked Delay	p. 154
Stability Analysis of Closed Networked Predictive Control Systems	p. 159
Realtime Simulation and Practical Experiment	p. 167
Practical Experiments	p. 167
Conclusion	p. 173
Analysis and Synthesis of NCSs with Random Feedback Delay	p. 177
Introduction	p. 177
Design of Networked Predictive Controller	p. 177
Stability of Networked Predictive Control Systems	p. 180
Constant Network Delay	p. 180
Random Network Delay	p. 186
Simulation & Experiments	p. 191
Numerical Simulation	p. 191
Practical Experiments	p. 191
Conclusion	p. 197
Analysis and Synthesis of NCSs with Random Forward and Feedback Delay	p. 199
Introduction	p. 199
Design of NPC Systems with both Forward and Feedback Network Delays	p. 199
Stability Criteria of Closed-Loop NPC Systems	p. 203
Constant Delays in both Forward and Feedback Channels	p. 204
Random Network Delay	p. 212
Simulation & Experiments	p. 217
Numerical Simulation	p. 217
Practical Experiments	p. 218
Conclusion	p. 222
Stochastic Analysis of NCSs with Random Delay and Data Dropout	p. 225
Introduction	p. 225
Predictive Control of Networked Systems	p. 225
Stochastic Stability of closed-Loop Networked Predictive Control Systems	p. 229
Examples	p. 236
Numerical Example	p. 236
Practical Experiments	p. 237
Conclusion	p. 242
Networked Data Fusion with Packet Losses and Variable Delays	p. 243
Introduction	p. 243
Problem Formulation	p. 245
Method of Data Fusion	p. 246
Recall of Federated Filters	p. 246
Stability of Networked Kalman Filtering	p. 248
Delay Data Processing	p. 250
Principle for Data Fusion	p. 261
Numerical Examples	p. 262
An Unstable Example	p. 262
A Stable Example	p. 266
Conclusion	p. 268
References	p. 271
Index	p. 283
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Lecture Notes in Control and Information Sciences

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