Modified gain-based lower bounds computation for the real structured singular value

In this paper, a modified gain-based algorithm (GBA) is presented to calculate the lower bound for the real structured singular Value (μ) problem. The basic idea of GBA is reformulating the real μ problem into a related worst-case disturbance-error performance problem, then the standard lower bound algorithm for worst-case performance assessment is used for calculation of maximizer uncertainty which maximizes the disturbance-error gain, and next this maximizer uncertainty can be used to obtain the lower bound for real μ. In the initial gain-based algorithm previously suggested by Pete Seiler etal, the way disturbance inserted and the error pulled off is from one channel to one channel. In this proposed modified algorithm, the error signal is still pulled off from one channel, however, the disturbance is inserted into from a linear combination (summation) of all channels, hence the effect of signals from all channels are reflected into the error signal. Several test problems indicate that the modified gain-based algorithm has a better performance for pure real μ problems.