Robust repetitive control of semi-Markovian jump systems

This paper considers the periodic reference tracking problem for continuous-time semi-Markovian jump systems. An observer-based robust $ H_{\infty } $ H∞ modified repetitive controller with logarithmically quantised output measurements is proposed. By using a lifting technique, the semi-Markovian jump system and the modified repetitive controller structure are transformed into a stochastic two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller structure. For the transformed 2D model, first, sufficient conditions are derived for the closed-loop control system to be mean square asymptotically stable by utilising tools from stochastic systems theory and multiple Lyapunov functional technique. Subsequently, a robust modified repetitive controller is synthesised to ensure a prescribed $ H_{\infty } $ H∞ attenuation performance in the presence of a bounded exogenous disturbance input. A numerical example on a switched boost converter circuit is considered and simulation results are provided to evaluate the proposed control strategy.