Gap metrics, representations, and nonlinear robust stability

Various alternative definitions for the nonlinear L/sub 2/- and /spl nu/-gap metrics are studied. The concept of /spl beta/-conjugacy and multiplicative homogeneity are introduced to relate the metrics to each other and to compare the stability margins of nonlinear feedback loops expressed in terms of the norms of complementary parallel projections. Left and right representations for the graph of a nonlinear system are studied. A new definition of "normalized" is introduced for left representations. Formulas for the gap metrics as the norm of the product of left and right representations are derived.