ANALYSIS OF PIECEWISE-LINEAR DC EQUATIONS.

The properties of dc equations with piecewise-linear characteristics are considered. The property of the set of mappings with piecewise-linear characteristics is investigated. The necessary and sufficient condition for the existence and uniqueness of dc solution is derived, and a more practical sufficient condition is derived by using the mu -function of a matrix. Using the mu -function, a sufficient condition is derived for numerical analysis by the Newton-Raphson method to globally converge to the unique dc solution in finite steps. An upper bound is given for the error between the dc and approximate solutions. From these results, the relation to the traditional differentiable case is clarified and the properties of piecewise-linear dc equations are more clearly stated.