Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form

For hybrid systems described by switched linear difference equations, linear threshold conditions, automata, and propositional logic conditions, described in mixed logical dynamical form, this note describes two algorithms for transforming such systems into an equivalent piecewise affine form, where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical. The proposed techniques exploit ideas from mixed-integer programming and multiparametric programming.