Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 61, Issue 11, Pages 3370-3385Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2016.2528050
Keywords
Contraction; linearization; Lyapunov methods; nonlinear control systems; synchronization
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We investigate how the following properties are related to each other: i) A manifold is transversally exponentially stable; ii) the transverse linearization along any solution in the manifold is exponentially stable; and iii) there exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.
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