Stability Robustness of Closed‐Loop Systems in Angular Metrics

H_∞‐norm is widely used in the analysis and synthesis of robust control, a field which continues to flourish and develop. However, H_∞‐norm can only be used to measure the distance between two stable systems, not unstable systems. Sometimes, it is not appropriate to measure the gap between two systems. In this paper, a new metric, angular metric, defined in linear spaces of real rational matrices, is used to measure the distance of two systems with different dimensions. It is also used to measure the uncertainties and describe the performance specifications of the robust control system. In the framework of this metric, the 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 structural robust stability and prove the necessary and sufficient conditions of the robust stability of the feedback control system.