Abstract: A time-varying discrete systems'state-space model and a cost function in the form of quadratic function were proposed in order to study the portfolio investment problem.This problem was under the considering of the discreteness of practical systems and the time-variation of the parameters.The H_∞ control theory with state feedback for time-varying discrete systems was applied to this new model.And a strategy of H_∞ control with state feedback for portfolio investment was also given.By using it,the purpose of the incensement of total assets according to the expected one could be achieved.

Key words: portfolio investment, time-varying discrete system, H_∞ control with state feedback