A suboptimal solution to constrained linear time varying quadratic regulation (CLTVQR)is proposed. In a neighborhood of the origin, the problem is formulated as a min-max LQRbased on polytopic inclusion of the dynamics in this neighborhood. Outside thisneighborhood, the control moves are obtained by solving a constrained finite horizonoptimization problem. The main contribution is to obtain a cost value arbitrarily close (butnot equal) to that of the optimal CLTVQR. The suboptimal CLTVQR preserves the feasibihtyof the optimal CLTVQR if and only if the min-max LQR exists feasible solution. By mildmodification, this suboptimal method can be applied to nonlinear systems.