Guaranteed cost control for bilinear systems by static output feedback

This paper proposes a static output feedback controller design technique for bilinear systems. Based on Lyapunov’s direct method, a nonlinear control law is derived to stabilize the system in the presence of external disturbances. Sufficient condition is derived in terms of a state-dependent nonlinear matrix inequality and then it is converted into a sum-of-squares (SOS) optimization problem. Semidefinite programming and SOS decomposition techniques are employed to solve the optimization problem. The obtained output feedback controller guarantees an upper bound of the performance index. The effectiveness of the proposed method is demonstrated through simulation results.