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Control of nonlinear systems is a multidisciplinary field involving electrical engineering, computer science, and control engineering. This book develops a systematic methodology to understand a quantitative stability result, which is an important contributor to nonlinear control systems' stability and performance. It focuses on the operator-theoretic approach, providing examples on how to apply it to network controlled systems. Current research results and the future of the operator-theoretic approach are also examined. Control theory engineers and applied mathematicians will find this work especially rewarding.