Abstract: The optimal control problem of the switched system,which subsystem is discrete linear system,is investigated.In the conditions of the given switched number and the quadratic performance function,the multi-periods decision-making problem can be resolved by being transformed into single decision-making problem.Genetic algorithm is used to search the switched instant to mimimize the performance function so that the optimal control problem of the switched discrete system can he obtain a analytic solution in global.A numerical example illustrates the effectiveness of the design approach.The simulation shows that the approach can resolve the optimal control problem of a kind of switched discrete.