The optimal switching problem is attracting plenty of attention. This problem can be considered as a special type of discrete optimization problem and is NP complete. In this paper, a class of optimal switching problem involving a family of linear subsystems and a quadratic cost functional is considered in discrete time, where only one subsystem is active at each time point. By deriving a precise lower bound expression and applying the branch and bound method, a computational method is developed for solving this discrete optimization problem. Numerical examples have been implemented to demonstrate the efficiency and effectiveness of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.