This note presents an optimal design method to enhance image quality in optical image stabilization (OIS) systems. First of all, performance limitations of conventional methods are shown and secondly, a new design framework based on convex optimization is proposed. The resulting controller essentially stabilizes the closed loop systems because the proposed method is derived from Lyapunov stability. From the test results, it is confirmed that this method reduces the effect of hand vibrations and makes images sharp. Additionally, it is shown that the proposed method is also effective in robot vision and recognition rate of deep neural network (DNN) based traffic signs and pedestrians detection in automotive applications. This note has three main contributions. First, performance limitations of the conventional method are shown. Second, from the relation between sensitivity and complementary sensitivity functions, an indirect design method for performance improvement is proposed, and finally, stability guaranteed optimal design is proposed. Unlike conventional methods, the proposed method does not require addition filters to suppress resonances of the plant and this note highlights phases of the closed loop systems on removing external vibrations.