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Characterizing points on discontinuity boundary of Filippov systems
(ACTA Press, 2008-01-01) Arango, I.; Taborda, J.A.; Arango, I.; Taborda, J.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
In this paper, we presented a basic methodology to understand the behavior of discontinuous piecewise smooth autonomous systems (denominated Filippov systems) in the planar neighborhood of the discontinuity boundary (DB). This methodology is useful in detection of nonsmooth bifurcations in Filippov systems. We propose a classification of the points and events on DB. This classification is more complete in comparison with the reported papers previously. The lines and the points are characterized with didactic symbols and the exclusive conditions for their existence based in geometric criterions. Boolean-valued functions are used to formulate the conditions. An illustrative example with a friction oscillator is presented.