Abstract
In this paper, we present some results on robustness of eigenvalue distribution in specified complementary regions for perturbed systems. If some eigenvalues of the nominal system are located in a specified region, the proposed sufficient conditions guarantee that the same number of eigenvalues of the perturbed system lie inside the same region. The characteristics of a linear time-invariant system are influenced by the eigenvalue location of the system matrix. Due to uncertainty or parameter variation, all mathematical descriptions of dynamic systems are approximate models at best. The effect of uncertainty will move the eigenvalues of a real system away from the designed ones. Therefore, it is significant to guarantee that the same number of eigenvalues of the perturbed system lie inside the same region as that of the nominal system. By the analysis of eigenvalue distribution, we can explore the locations of dominant eigenvalues, specified eigenvalues or even individual eigenvalues of perturbed systems. Consequently, more properties of perturbed systems such as stability margin, performance robustness and so on can be examined. The proposed theorems can be applied to both continuous- and discrete-time systems. In addition, the analysis of stability robustness can be dealt with as a special case in our study. Two examples are given to show the applicability of the proposed theorems. Finally, some conclusions are presented.
