Gain‐phase information based robust control theory

Summary This article presents new approaches for analyzing and designing the robust control system by using both the gain and phase information. These approaches aim to relax the stability condition and further improve the system performance than the H∞‐robust control theory. The contributions of this article are: (i) to propose a new gain‐phase (GP‐) robust stability theorem which can further relax the stability condition than the small‐gain theorem by using both the gain and phase information of uncertainty, (ii) to propose a new GP‐mixed sensitivity problem which can further improve the system performance than the mixed sensitivity method by using the GP‐robust stability theorem instead of the small‐gain one, (iii) to develop the WΩ‐K iteration algorithm to solve the GP‐mixed sensitivity problem and to verify the effectiveness of the proposed method through the design example of automotive fuel control system, and (iv) to formulate a new Ψ‐control problem with phase optimality criterion and an H∞/Ψ‐mixed control problem with both the gain and phase optimality criteria, to derive their solution for SISO output feedback systems and to show their effectiveness through two design examples.