This paper addresses the problem of robust H-2 and H-infinity control of discrete linear time-invariant (LTI) systems with polytopic uncertainties via dynamic output feedback. The problem has been known to be difficult when a parameter dependent Lyapunov function is to be applied for a less conservative design due to non-convexity. Our approach is based on a novel bounding technique that converts the non-convex optimization into a convex one together with a line search, which is simple but may be conservative. To further reduce the design conservatism, an algorithm based on the sequentially linear programming method (SLPMM) is proposed. A numerical example is given which demonstrates the feasibility of the proposed design methods.