In this paper, the robust linear quadratic regulation problem with cheap control is studied for the uncertain systems with norm-bounded uncertainty and integral quadratic constraint uncertainty, respectively. A Riccati equation approach is employed as a tool to investigate the limiting case in which a scalar weighting coefficient on the control input in the quadratic cost functional approaches zero. The corresponding performance limit is derived. Some results about monotonicity properties and the limiting behavior of the minimal positive definite solution to the Riccati equation are given. Using the limiting behavior of the minimal positive definite stabilizing solution to the Riccati equation, we find that perfect regulation with cheap control can be achieved if the uncertain system has a particular structure.