Fuzzy supervisor approach on logic-based switching H 2 / H ∞

Abstract

Abstract

In this paper the synthesis of a logic-based switching H ₂/H _∞ state-feedback controller for continuous-time linear time-invariant (LTI) singular perturbation systems is considered which achieves a minimum limit on the H ₂ 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 linear matrix inequality (LMI)-based formulation of the fast and slow subsystem controllers leads to a ε-independent structure which ensures a good performance in both the transient phase and the steady-state phase. 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 (controller) changing. Simulations show that the proposed non-linear scheme composed of two low-order controllers improves the performance in comparison with the linear optimal scheme with higher order designed for a full-order system.