In dynamic systems， optimal switching for switched systems is a typical NPhard problem in discrete time，this paper considers a class of linear switched systems with constraints. In order to find the global optimal solution， by analyzing the dynamic constraint and the linear performance of the system， we construct the dynamic lower bounds of the constraint and the objective function， respectively. These lower bounds provide an accelerated rule for tree search methods. Therefore， a depthfirst branch and bound algorithm are proposed. The method can exactly find the global optimal solution of the dynamic system. The numerical experiment shows the effectiveness and efficiency of the proposed method.