Logic based switching H2/H∞ controller design for linear singular perturbation systems: A fuzzy supervisor approach

Abstract

In this paper the synthesis of logic-based switching H2/H∞ state-feedback controller for continuous-time LTI singular perturbation systems 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 two controllers. A convex LMI-Based formulation of the two fast and slow subsystem controllers leads to a 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.