We study in this paper the linear-quadratic (LQ) optimal control problem of discrete-time switched systems with a constant switching cost for both finite and infinite time horizons. We reduce these problems into an auxiliary problem, which is an LQoptimal switching control problem with a cardinality constraint on the total number of switchings. Based on the solution structure derived from the dynamic programming (DP) procedure, we develop a lower bounding scheme by exploiting the monotonicity of the Riccati difference equation. Integrating such a lower bounding scheme into a branch and bound (BnB) framework, we offer an efficient numerical solution scheme for the LQ switching control problem with switching cost. (C) 2012 Elsevier Ltd. All rights reserved.