The design of H. control methodology for non-linear systems to guarantee the tracking behaviour in the sense of input-output spheres

A general non-linear system usually contains some uncertainties, such as plant parameter variations and uncertain inputs, which may make desired system performance hard to be achieved or even cause the closed-loop system unstable. An H control design methodology based on the tracking behaviour in the sense of input-output spheres is proposed in this study to ensure that the system output is bounded in the desired output sphere while an uncertain input, which is described in an input sphere, is applied to the system. The loop-shaping technique is applied in the proposed design procedure to guarantee the system robustness against disturbances and uncertainties. To attest the feasibility of the proposed methodology, a non-linear inverted pendulum is then studied. The computer simulation results reveal that the proposed methodology can achieve the desired performance with good tracking behaviour in the sense of input-output spheres by effectively rejecting the disturbances and uncertainties of this system.