Complex and real performance radii and their computation

This paper considers the problem of robust performance of a linear time-invariant system in ℋ_∞ norm. The concepts of complex and real performance radii are introduced to describe the smallest size of dynamic or parametric perturbations to a feedback system that either destabilize the system or destroy a performance bound in certain closed loop transfer matrix of the system. An algorithm to compute the complex performance radius is given. For the real performance radius, a lower bound, which often turns out to be exact, is obtained