Three-Stage Feedback Controller Design with Applications to a Three Time-Scale System

A new technique was presented that facilitates design of independent full-state feedback controllers at the subsystem levels. Different types of local controllers, for example, eigenvalue assignment, robust, optimal (in some sense L-1, H-2, H-infinity,...) may be used to control different subsystems. This feature has not been available for any known linear feedback controller design. In the second part of the paper, we specialize the results obtained to the three time-scale linear systems (singularly perturbed control systems) that have natural decomposition into slow, fast, and very fast subsystems. The proposed technique eliminates numerical ill-condition of the original three-time scale problems.