Robust finite frequency H∞ control for Lipschitz nonlinear systems

Abstract

This paper is concerned with the [Formula: see text] control problem for Lipschitz nonlinear systems in the finite-frequency domain. Both parameter uncertainties and external disturbances are considered. In contrast to existing full-frequency methods, the proposed approach takes into account of the frequency information of disturbances during the design proceeding. Sufficient analysis conditions for the closed-loop system are firstly derived. Then, synthesis conditions are formulated in terms of linear matrix inequalities (LMIs). In fact, the control gain is designed to attenuate the influence of disturbances in different frequency ranges (low, middle and high). Finally, the model of the Chua circuit is used to validate the effectiveness of the proposed finite-frequency approach and to prove its superiority compared to the full-frequency counterpart.