# Angular velocity nonlinear observer from vector measurements

**Authors:**L. Magnis, N. Petit, Automatica, Vol 75, pp. 46-53, January 2017. DOI: 10.1016/j.automatica.2016.09.027

We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified Kirchhoff law incorporating a damping term αut with a coefficient α that may depend on the node is considered. We show that for a convenient choice of the sequence of coefficients α, any solution of the wave equation on the network becomes constant after a finite time. The condition on the coefficients proves to be sharp at least for a star-shaped tree. Similar results are derived when we replace the transparent boundary condition by the Dirichlet (resp. Neumann) boundary condition at one external node. Our results lead to the finite-time stabilization even though the systems may not be dissipative.

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**BibTeX**

@Article{2017-01-23,

author = {N. Petit L. Magnis},

title = {Angular velocity nonlinear observer from vector measurements},

journal = {Automatica},

volume = {75},

number = {},

pages = {46-53},

year = {2017},

}