Stability robustness of control system in angular metric

The robust control theory based on ∞-norm is the successful example of solving the robust control problem, which has become a fairly systematic theory. However, ∞-norm can only be used to measure the distance between two stable systems not the unstable systems. Sometimes, it is not appropriate to measure the gap of two stable systems. A new metric, angular metric, is defined in linear spaces of real rational matrices, which can measure the uncertainties and describe the performance specifications of the robust control system. In the framework of this metric, robust stability margin is proposed to characterize the stability robustness of the closed-loop system. When both the plant and the controller have uncertainties simultaneously, we introduce the structural robust stability, and prove the necessary and sufficient conditions of the robust stability of the feedback control system.