Synthesis of switching H2 and H∞ output-feedback controllers: A fuzzy supervisor approach

In this paper the synthesis of switching multiple static output-feedback controllers for discrete-time LTI systems with state-multiplicative noise is considered which achieves a minimum bound on either the stochastic H₂ or the H_infin performance levels. 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 tracking performance in both the transient state (H₂) and the steady state (H_infin). 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.