This paper studies the discrete-time linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS problem. Based on the particular structures of these analytical expressions, an efficient algorithm suitable for solving an arbitrary DLQRS problem is proposed. Simulation results indicate that the proposed algorithm can solve randomly generated DLQRS problems with very low computational complexity. The theoretical analysis in this paper can significantly simplify the computation of the optimal strategy, making an NP hard problem numerically tractable.
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