Synthesis of low-coefficient sensitivity controllers with respect to multiplicative controller coefficient variations

In this study, a set of optimal state-space descriptions with minimum H_∞-sensitivity to multiplicative controller coefficient variations and a desirable disturbance attenuation level is synthesised for discrete-time linear systems. The first aim is to present a new strategy to evaluate the H_∞-sensitivity of the transfer function to multiplicative controller coefficient variations. The H_∞ norm of the sum of coefficient sensitivity functions is regarded as an H_∞-sensitivity measure. The second contribution is to present less conservative conditions to design low-sensitivity controllers via minimisation of the H_∞-sensitivity measure. In addition, a linear matrix inequality-based algorithm is developed to obtain the controller gain matrices. Finally, two numerical examples which demonstrate the effectiveness and advantages of the proposed method are presented.