Gap metrics, representations, and nonlinear robust stability

M. R. James; M. C. Smith; G. Vinnicombe

doi:10.1109/CDC.2000.914262

Gap metrics, representations, and nonlinear robust stability

M. R. James, M. C. Smith, G. Vinnicombe

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Various alternative definitions for the nonlinear L₂- 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 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.

Original language	English
Pages (from-to)	2936-2941
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	3
DOIs	https://doi.org/10.1109/CDC.2000.914262
Publication status	Published - Dec 2000

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KW - Graph representations

KW - Nonlinear systems

KW - Robust control

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JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

ER -

Gap metrics, representations, and nonlinear robust stability

Abstract

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