Robust decentralized eigenvalues clustering for multi-time-scale systems with perturbations

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, consisting 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 slow subsystem and the uncertain fast subsystems with the parameter perturbations. An algorithm for the design of a decentralized robust state feedback controller for multitime-scale systems is then presented. It not only ensures that the eigenvalues of these subsystems are located in the desired regions, but also makes sure that all the eigenvalues of the whole system are in our desired regions. An illustrative example is adopted, and the result is satisfactory.