A New Algorithm for Gap Metric Calculation Based on Frequency Response Data

The gap metric is a very essential tool for robust stability analysis of control systems and fault tolerant control. It is widely calculated as a model base. However, it is challenging to derive a precise mathematical model that accurately represents the real system. Consequently, the validity of the gap computation based on the model can not be guaranteed. Therefore, development of different approaches for gap calculation becomes more serious. Motivated by the aforementioned problem, we introduce a new algorithm for gap computation based on frequency response data. The data will be recorded in the time domain and then converted to the frequency domain using the fast Fourier transform. The frequency response data easily can be represented in the Euclidean plane and hence the gap at each frequency can be calculated since the the gap is the angular measure distance between two systems. Subsequently, the algorithm is constructed using the geometric interpretation of the gap and some properties of normed vector spaces. A comparative study with a model base is provided to demonstrate the effectiveness of the proposed algorithm.