The fundamental dominance condition for MIMO systems with parametric uncertainty

The fundamental dominance condition, an improved diagonal dominance measure in the sense that it is weaker than the classical row/column dominance measures, is developed in this paper for MIMO systems with parametric uncertainty and polytopic uncertainty bounds. It is shown that the study of this dominance condition is equivalent to the study of polynomial families. Hence, well established tools dealing with the problem of locating the roots of an entire family of polynomials can then be used to produce a simple graphical solution to the dominance problem. Two examples are used to illustrate the proposed method. Finally, a simplified direct Nyquist array based stability theorem is developed for uncertain, square MIMO systems having affine linear perturbation structure.