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On a topological condition for strongly asymptotically stable differential inclusions
Description
In this paper, we will show that a system on a non-contractible manifold cannot be strongly asymptotically stabilized in Filippov’s sense, even if discontinuous feedback is used. The fact is well-known for C1feedback case, and we extend it to the discontinuous feedback case. To consider the stabilization problem on a non-contractible manifold, the assumption convexity or upper semicontinuity is restrictive. We will propose a new type of differential inclusion without upper semicontinuity by defining a function indicating a rate of leaving from discontinuous set. By adopting the new differential inclusion, stabilization problems on non-contractible manifolds become possible for many cases.
Journal
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- Proceedings of the 44th IEEE Conference on Decision and Control
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Proceedings of the 44th IEEE Conference on Decision and Control 5444-5449, 2006-10-04
IEEE
