Robustness analysis of singularly perturbed system

The authors formulate a singularly perturbed system into a standard μ-interconnection framework by using linear fractional transformations. They derive a set of stability conditions for the system by defining the (real) structured singular value (μ) of a corresponding matrix while the exact solution of the ∈-bound is characterized. The results are presented on the two-time-scale case for simplicity; their developments are extensible to the multiple time-scale case. The proposed approach may provide great potential for robust controller synthesis and the robust performance analysis of output feedback singularly perturbed systems