I. Introduction
In model-based syntheses, a mathematical model is firstly constructed using input/output data sets obtained from a plant. Secondly, a controller is designed based on the model. The model-based design is widely used in the industrial field since it can evaluate stability of the closed-loop system and control performance before the controller is implemented. Above all, the loop shaping method [1] is known to achieve good control performance and robustness, and a lot of applications have been reported, e.g., [2]–[5]. In this method, controller design consists of two steps; designs of weighting functions and a stabilizing controller. The stabilizing controller is designed to minimize the norm of the transfer matrix consisting of four closed-loop transfer functions such as a sensitivity function, a complementary sensitivity function, etc. As a result, the closed-loop system achieves good tracking and robustness if suitable weighting functions are designed. Moreover, the closed-loop system is constructed as a well-balanced system for disturbances injected from both input and output sides if the plant is a MIMO system. However, if weighting functions are not suitable, the stabilizing controller may change the gain characteristic of the open-loop function to improve robust stability margin. In this case, design of weighting functions is often required in terms of achieving desired performance.