A cutting plane algorithm for frequency domain specification with application to bending modes attenuation

Bending modes attenuation is a very challenging problem, especially if the modes are close to the bandwidth, in which case applying weighting filters is useless. This work aims to present an idea based on the cutting plane algorithm (CPA) to overcome such problems. The interesting point of using CPA instead of optimization under LMI (linear matrix inequality) constraints is that no additional variables are introduced, which has a significant effect on the computation time. The application of Youla parameterization is considered in order to restore the linearity in the compensator parameters, thus the convexity is guaranteed and the CPA is efficiently used.