Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign

This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.