H_inf optimal sampled-data controller synthesis with generalised disturbance and performance channels

Discrete-time controllers, implemented on digital platforms, are generally used to control continuous-time plants using sampled measurements. In this paper, a tractable sampled-data controller synthesis method is proposed for linear time-invariant plants. The proposed method gives guarantees for stability and performance of the closed-loop system in terms of the ${\mathcal{H}_\infty }$-norm, while taking the effect of sampling explicitly into account. This is done by taking a hybrid systems approach, which allows formulating linear matrix inequalities using the explicit solution to a Riccati differential equation. Furthermore, the sampled-data problem formulation is extended so that continuous-time design techniques like ${\mathcal{H}_\infty }$ loop-shaping can be used in a sampled-data context. To do so, it is essential to consider generalised disturbance and performance channels, where both discrete and continuous signals are weighted using weighting filters. The controller design method is demonstrated on an academic example and on a more practical example of reference tracking of a two-mass-spring-damper system.