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Journal Articles IEEE Transactions on Automatic Control Year : 2017

Immersion and invariance stabilization of nonlinear systems via virtual and horizontal contraction

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Lei Wang
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  • PersonId : 943497
R. Ortega
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  • PersonId : 848065
Zhitao Liu
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  • PersonId : 1059011
Hongye Su
  • Function : Author

Abstract

The main objective of this paper is to revisit one of the key steps of immersion and invariance stabilizing controller design. Namely, the one that ensures attractivity of the manifold whose internal dynamics contains a copy of the desired system behavior. Towards this end we invoke contraction theory principles and propose two alternative procedures to carry out this step: (i) to replace attractivity of the manifold by virtual contraction of the off-the-manifold coordinate and (ii) to ensure the attractivity of the manifold rendering it horizontally contractive. This makes more systematic the design with more explicit degrees of freedom to accomplish the task. Several examples, including the classical case of systems in feedback form, are used to illustrate the proposed design.
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Dates and versions

hal-01815976 , version 1 (17-06-2020)

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Lei Wang, Fulvio Forni, R. Ortega, Zhitao Liu, Hongye Su. Immersion and invariance stabilization of nonlinear systems via virtual and horizontal contraction. IEEE Transactions on Automatic Control, 2017, 62 (8), pp.4017-4022. ⟨10.1109/tac.2016.2614888⟩. ⟨hal-01815976⟩
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