(Georgia Institute of Technology, 2008-01-26)
Dieci, Luca; Lopez, Luciano
In this report, we have collected notes of work done during the Academic Year 2006-07, while the second author was in visit at Georgia Tech. Our main goals are the following: to reinterpret the 1st order theory of Filippov and to propose second author corrections to the theory; to provide a systematic, and non-ambiguous way to define the vector field on the intersection of several surfaces of discontinuity, consistent with Filippov's construction; to propose, and implement, numerical methods to approximate a trajectory of systems with discontinuous right-hand sides, and to illustrate their performance on a few examples.