A generalized Padé approximation of time delay operator

This paper addresses the problem of fractional order Pade approximation for the time delay operator. Based on optimization method, a fitting polynomial with basic order α is constructed to approximate the time delay operator. This makes for two generalized Pade approximations in the form of normal and symmetric approximation, respectively. The advantage of the proposed method lies in the fact that the resulting approximate model is in the standard transform function form of any commensurate order α, making all of the existing stability analysis methods and control design tools for such systems amenable to the fractional order time delay systems. Some numerical examples are given to demonstrate the effectiveness of the proposed method.