Limits of Stability and Stabilization of Time-Delay Systems: A Small-Gain Approach

Description

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. Front Matter ....Pages i-xvi Introduction (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 1-19 Mathematical Background (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 21-42 Small-Gain Stability Conditions (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 43-70 Delay Margin (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 71-93 Stabilization of Linear Systems with Time-Varying Delays (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 95-107 Delay Margin Achievable by PID Controllers (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 109-143 Delay Radius of MIMO Delay Systems (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 145-165 Stabilization of Networked Delay Systems (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 167-186 Consensus of Multi-agent Systems Under Delay (Jing Zhu, Tian Qi, Dan Ma, Jie Chen)....Pages 187-208 Back Matter ....Pages 209-219