Eigenvalues Assignment Robustness in Specified Regions for Uncertain Multi-Time-Scale Systems

Abstract

From the viewpoint of the eigenvalues locations of the multi-time-scale systems, we realize that the eigenvalues positions of the fast subsystems are far from the slow subsystem ones, and the uncertainty or parameter variation will move the eigenvalues of a nominal system away from the desired ones. Therefore, it is significant to guarantee that the eigenvalues of the perturbed system lie inside our desired regions as those of the nominal system. The multi-time-scale system under structured perturbation is considered in this paper. We present some sufficient conditions for the robustness measures of eigenvalues assignment in the specified regions. A design algorithm by the method of constraint optimization to design a robust decentralized controller to assign the eigenvalues of whole multi-time-scale system is also provided in this research. An illustration example is presented to show the applicabilityof our proposed theorems.