Design of distributed robust control of 1D-spatially interconnected systems in the repetitive process setting

In this paper we consider the $\mathcal{H}_{\infty}$ controller design problem for uncertain differential linear repetitive processes via full order dynamic output feedback controllers. The existence condition of desired robust $\mathcal{H}_{\infty}$ controllers is expressed as a feasibility problem of a linear matrix inequality (LMI). Then it is shown that the developed results can be applied to robust distributed controller design for 1D-spatially interconnected systems that are composed of several linear continuous-time subsystems, where each directly interacts with neighbouring subsystems. A simulation based case study on the model of a vehicle platoons system is given to demonstrate the feasibility and effectiveness of the new designs.