Synthesis of a Logic-Based Switching H2/H∞ Controller:A Fuzzy Supervisor Approach

In this paper, the synthesis of switching H2/H∞ controller is considered which achieves a minimum bound on the H2 performance level, while satisfying the H∞ performance. The proposed hybrid control scheme is based on a fuzzy supervisor which manages the combination of controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good performance in both the transient phase (H2) and the steady phase (H∞). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the system with the proposed controller remains globally stable despite the configuration changing. The conservatism introduced by means of the proposed methodology is significantly decreased in comparison to the Lyapunov shaping methods which oblige the designer to employ a common Lyapunov matrix for all the performance criteria and design one controller that satisfy all the objectives. The results of the common H2/H∞ methods can be derived from proposed method easily.