James, MatthewSmith, M CVinnicombe, G2015-12-132015-12-130363-0129http://hdl.handle.net/1885/81320Various alternative definitions for the nonlinear H2-, L 2-, and v-gap metrics are studied. The concept of β-conjugacy and multiplicative homogeneity are introduced to relate the metrics to each other and to compare the stability margins of nonlinear feeKeywords: Feedback; Graph theory; Hydrogen; Mathematical operators; Nonlinear systems; Optimization; Problem solving; System stability; Controller synthesis; Gap metric; Graph representations; Information states; Nonlinear H control; Robustness (control systems) Controller synthesis; Gap metric; Graph representations; Information states; Nonlinear H? control; Nonlinear systems; Robust control200510.1137/S03630129013930672015-12-11