Explicit formulas for the solutions of piecewise linear networks

A methodology is presented for obtaining explicit formulas for the solution of class-P piecewise linear (PL) networks and, inherently, for the linear complementary problem (LCP). The method uses the [.] operator, which has been previously defined in the literature to extend the explicit PL model descriptions of Chua. An important consequence of the methodology is that it proves that class-P networks have explicit solutions.