Limits of Stability and Stabilization of Time-Delay Systems

1. Front Matter

   Pages i-xvi

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2. Introduction

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 1-19

3. Mathematical Background

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 21-42

4. Small-Gain Stability Conditions

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 43-70

5. Delay Margin

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 71-93

6. Stabilization of Linear Systems with Time-Varying Delays

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 95-107

7. Delay Margin Achievable by PID Controllers

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 109-143

8. Delay Radius of MIMO Delay Systems

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 145-165

9. Stabilization of Networked Delay Systems

   • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

   Pages 167-186

10. Consensus of Multi-agent Systems Under Delay

    • Jing Zhu, Tian Qi, Dan Ma, Jie Chen

    Pages 187-208

11. Back Matter

    Pages 209-219

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This authored monograph presents a study on fundamental limits and robustness of stability and stabilization of time-delay systems, with an emphasis on time-varying delay, robust stabilization, and newly emerged areas such as networked control and multi-agent systems. The authors systematically develop an operator-theoretic approach that departs from both the traditional algebraic approach and the currently pervasive LMI solution methods. This approach is built on the classical small-gain theorem, which enables the author to draw upon powerful tools and techniques from robust control theory. The book contains motivating examples and presents mathematical key facts that are required in the subsequent sections. The target audience primarily comprises researchers and professionals in the field of control theory, but the book may also be beneficial for graduate students alike. 

• Small gain stability conditions
• Uncertainty modeling
• Delay margin
• Stabilization of linear systems
• Delay radius of MIMO delay systems
• Networked delay systems

• College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

  Jing Zhu

• Center for Control and Optimization, South China University of Technology, Guangzhou, China

  Tian Qi

• College of Information Science and Engineering, Northeastern University, Shenyang, China

  Dan Ma

• Department of Electronic Engineering, City University of Hong Kong, Hong Kong, Hong Kong

  Jie Chen

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