Sliding Mode Controllers for Uncertain Systems with Input Nonlinearities

the filter is represented by the dotted line. The equivalent structure with the filter was obtained by scaling the disturbance input, according to Eq. (6), and the magnitude of its transfer function is shown in Fig. 2, as a dashed line. It is clear from that figure that the structure with the filter and the structure with the scaled disturbance input have very similar frequency characteristics, and their norms are ||G||oo = 2.6903 and ||G||2 = 453.2945 for the structure with the filter and HGIL = 2.6911 and ||G||2 = 453.5661 for the structure with the scaled disturbance input. Two frequency weighted H^ controllers for this structure were designed. The first one is based on the structure with a filter, whereas the second is based on the structure with scaled input matrix. The openand closed-loop transfer functions are shown in Fig. 3. The closed-loop performance of the structure with the filter and that with the scaled input is almost identical. The closed-loop H^ norms are as follows: HG^I^ = 0.09681 for the structure with the filter and || Gci || oo = 0.09676 for the structure with the scaled disturbance input. In a similar manner, H2 controllers were designed. The closedloop H2 norms are as follows: ||Gci||2 = 108.6295 for the structure with the filter, and ||Gci||2 = 108.7181 for the structure with the scaled disturbance input.