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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.

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

Introduction.- Mathematical Background.- Small-Gain Stability Conditions.- Delay Margin.- Stabilization of Linear Systems with Time-Varying Delays.- Delay Margin Achievable by PID Controllers.- Delay Radius of MIMO Delay Systems.- Stabilization of Networked Delay Systems.- Consensus of Multi-Agent Systems under Delay.