Robustness with real parametric and structured complex uncertainty

Abstract

The problem of robust stability and performance in feedback control systems with n real (possibly repeated) uncertain parameters and structured unmodelled dynamics, the latter taking the form of m complex blocks dynamic uncertainties is considered. A robustness margin r_m is defined with respect to such model uncertainty structure and an algorithm is developed to compute it. Robust stability and performance is characterized in terms of r_m in much the same way as with the Multivariate Stability Margin k_m or the Structured Singular value μ. An iterative procedure employing the above algorithm is given to compute tight bounds on k_m and μ. These bounds are exact for the case m ≤ 3.