Abstract

\[ A_i+\sum\delta_{ij}D_{ij}, \] where the matrices \(B_{ij}\) are known and the parameters \(\delta_{ij}\) are unknown. In particular, for case (1), when \(A_0\) is a Metzler matrix (i.e., all the off-diagonal elements are nonnegative) and, in addition, the matrices \(A_i\), \(D_{ij}\) and \(E\) are nonnegative, they prove that the complex radius and the real radius coincide, and characterize it in terms of the norms of the transfer matrices \(G_{ij}=EH^{-1}D_{ij}\). Similar results are given for the case (2). Applications to time delay differential systems are discussed in the last section.