Robust output regulation of uncertain linear fractional transformation systems with application to non‐linear Chua's circuit

Abstract

This study deals with the robust H ∞ output regulation problem for a class of uncertain systems in a linear fractional transformation form. The problem is addressed under a measurement output-feedback framework, i.e. no full information of both plant and exosystem states is assumed for feedback control use. A new robust control law with a novel output regulator structure is proposed, based on which sufficient conditions for robust output regulability and L 2 stability are established in terms of linear matrix equations plus a set of linear matrix inequalities. As a result, the optimal H ∞ output regulation control solution can be synthesised effectively via convex optimisation. Finally, the proposed robust output regulation design scheme will be applied to solve the chaos tracking control problem for the non-linear Chua's circuit.