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Nonlinear controllability and observability with applications to gradient systems

By José Agostinho Basto Gonçalves

Abstract

We extend the theory of nonlinear observability due to Hermann-\ud Krener [5] to the non-regular case, in which the observability codistribution\ud is not constant dimensional, and we obtain results in\ud some sense dual of the ones already known for accessibility.\ud We discuss a conjecture of P. Varaya [15], namely that the\ud isomorphism of two locally controllable gradient systems is an isometry\ud for the underlying pseudo Riemannian manifolds, proving it to be false\ud without further, or different, assumptions; we also prove some positive\ud results, and the analogue of the above for Hamiltonian systems, with\ud weaker conditions: an isomorphism of reachable Hamiltonian systems is\ud a symplectomorphism.\ud Finally we prove that a Hamiltonian system with finite-dimensional\ud Lie algebra, satisfying standard conditions, has an accessible Hamiltonian\ud realization, constructed in a canonical way

Topics: QA
OAI identifier: oai:wrap.warwick.ac.uk:3496

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