Computation of real structured singular value by Stability Feeler

The real structured singular value mu is effective for robust stability analysis of systems with structured uncertainty. Several methods for obtaining upper bounds of mu have been proposed. However, it is difficult to obtain the true value of mu. In this paper we propose a calculation method for real structured singular value mu by Stability Feeler, which is a new robust stability analysis tool proposed by the authors. While we need to obtain stability intervals of multiple parameters for real mu-analysis, it is possible by using Stability Feeler and the bisection method. Linearization is also needed for real mu-analysis by Stability Feeler. The conservativeness of the result, however, can be reduced by using a region splitting and expanding method. A numerical example shows that the proposed method can give an upper bound and a lower bound of mu, which almost coincide with the true value of mu. The conservativeness of the obtained result is less than the previous ones. The authors believe that this method can generally give the results, which almost coincide with the true value of mu if region splitting is done by sufficiently small splitting rate.