Detecting Sliding Areas in Three-Dimensional Filippov Systems using an Integration-Free Method
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2008-01-01
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WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC
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In this paper, we detect sliding areas in three-dimensional (3D) Filippov systems using an integration-free method denominated Singular Point Tracking (SPT). Many physical applications in engineering can be modelled as Filippov systems. Sliding dynamics due to nonsmooth phenomena as friction, hysteresis or switching are inherent to Filippov systems. The analysis of sliding dynamics has many mathematical and numerical difficulties. Several well-known numerical problems can be avoid using integration-free methods. In this paper, we extend the SPT method to 3D Filippov systems. In comparison with the 2D case, the evaluation of the vector fields on the discontinuity boundary (DB) should be reformulated and new dynamics on DB should be characterized.