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Piecewise linear continuous time systems, i.e..piecewise linear ODEs are a typical class of piecewise smooth systems, which are extensively used to model many physical phenomena.Because piecewise smooth systems are non-differentiable and even discontinuous, the methods from the differentiable dynamical systems theory cannot be applied directly and specific approaches have to be pursued.Although explicit solutions to a piecewise linear continuous time system can be obtained in each region where one linear system is defined, gluing these solutions globally at the discontinuity boundaries to get a whole picture of the piecewise linear continuous time system is a hard problem, and the theory for piecewise linear continuous time systems is also in its infancy.