Diagonal dominance for robust stability of multivariable interval systems

We consider the problem of robust stability of a MIMO feedback system in the presence of parametric perturbations. More specifically, we consider the case when the entries of the system transfer matrix are interval plants, i.e. transfer functions whose numerator and denominator are interval polynomials. Although it is clear that the special structure of this problem can be exploited in the general μ analysis structured perturbations framework, nevertheless it turns out that even for relatively simple cases it may be difficult to obtain reliable bounds. In this paper we take a different approach to the problem. The basic tool used to assess robust stability is a sufficient condition for stability, known as ´diagonal dominance´ condition, which is nevertheless much easier to check than the structured singular value condition. The paper shows that the robust diagonal dominance test can be carried out by plotting a finite number of frequency plots, a number of which correspond to extremal transfer functions of the transfer matrix, while others are obtainable by easy, analytic manipulations on the entries of the system matrix