An Efficient Technique for Computing a Sub-optimal Disturbance Attenuation $H_{infty}$ Control Problem Feedback Solution

This paper presents a technique to determine the optimal H_infin state-feedback control gain. This gain leads to a closed loop system with the best level of disturbance attenuation. The proposed method uses convergence characteristics of the bisection method and iterative solutions of algebraic Riccati equations (AREs). The numerical instability monitoring of the AREs and Lyapunov equation solutions are used as a tool to adjust the level of disturbance attenuation. The technique uses the fact that Lyapunov equation solutions can present low-rank characteristics and that numerical aspects, such as products involving inverse of matrices, can be efficiently implemented. Tests carried out on three dynamic systems, including one of 3078 states, demonstrate the efficiency of the proposed method.