Multiple Robust H∞ Controller Design Using the Nonsmooth Optimization Method

This paper proposes a systematic technique to design multiple robust H∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets, and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problems. A numerical example shows that the proposed multiple robust control method can improve the closed loop performance when a single robust controller cannot achieve satisfactory performance.