Eigenvalues assignment robustness in specified regions for uncertain multi-time-scale systems

From the viewpoint of the eigenvalues locations of the multi-time-scale sys tems, we realize that the eigenvalues positions of the fast subsystems are far from the slow subsystem ones, and the uncertainty or parameter variatio n will move the eigenvalues of a nominal system away from the desired ones. Therefore, it is significant to guarantee that the eigenvalues of the pert urbed 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 measu res of eigenvalues assignment in the specified regions. A design algorithm by the method of constraint optimization to design a robust decentralized c ontroller to assign the eigenvalues of whole multi-time-scale system is als o provided in this research. An illustration example is presented to show t he applicability of our proposed theorems.