The formulation of the robust decentralized eigenvalues clustering with the
design technique of the decentralized robust state feedback controller for
multi-time-scale systems is facilitated. The multi-time-scale system, cons
isting of a slow subsystem and some fast subsystems with perturbations, is
considered. From the eigenvalues locations of the multi-time-scale system,
it is known that the locations of the fast subsystems are far from the slow
subsystem ones. Furthermore, presented here are some sufficient conditions
of robust eigenvalue clustering in specified regions for the uncertain slo
w subsystem and the uncertain fast subsystems with the parameter perturbati
ons. An algorithm for the design of a decentralized robust state feedback c
ontroller for multi-time-scale systems is then presented. It not only ensur
es that the eigenvalues of these subsystems are located in the desired regi
ons, but also makes sure that all the eigenvalues of the whole system are i
n our desired regions. An illustrative example is adopted, and the result i
s satisfactory.