Abstract: Resorting to the bounded optimization method and the differential game theory, the paper deals with the minimax control problems of periodically time-varying linear system with norm-bounded exogenous disturbance and the system with parameter perturbation. The sufficient conditions for the solubility are that some Riccati differential equation admits a stabilizing solution, some additional condition about the worst disturbance or perturbation is satisfied, and the minimax control (if exists) turns out to be a linear state feedback. Moreover, the guarantee value of cost functional for the closed-loop system is presented.