Synthesis of control laws with specified gain and phase margin and poles region

The paper presents a method of synthesising a state-feedback control law which yields a closed-loop system with specified robustness characteristics and meanwhile ensures all closed-looppoles inside a circular region, centred at (e, 0) with radius r, where |e| + r ¿¿ 1. This robustness can be interpreted as gain and phase margins when a cone-bounded nonlinearity is introduced in the loop. The condition imposed on the robustness sector, so that the feedback control will be optimal with respect to a quadratic performance index, is also obtained.