Gain characteristics estimation for data-driven control design and extension theorem

Estimate of the gain characteristics of systems by using a transient response is essential for the development of our data-driven loop shaping method, and we have proposed an estimation method using a filterbank. Estimate of the l
₂
gain is also essential for model validation and the extension theorem gives the theoretical basis. In this paper, the relationship between our estimation method and the l
₂
gain estimation method based on the extension theorem is clarified, and a method for a proper setting of bandpass filter parameters is proposed. Further, the l
₂
gain estimates by using these methods are compared in accuracy, efficiency, and robustness against noise by numerical experiments.