Comparison Theorems for Viscosity Solutions of a System of Quasivariational Inequalities with Application to Optimal Control with Switching Costs

In this paper we prove a comparison principle between a viscosity sub- and supersolution for a system of quasivariational inequalities and apply it to show that a continuous lower value vector function of an optimal switching-cost control problem is characterized as the minimal, nonnegative, continuous, viscosity supersolution of the SQVI.