On the l₂-induced control for eventually periodic systems

This paper is focused on the l₂-induced control of eventually periodic linear discrete-time systems. We prove for such systems that a synthesis exists if and only if an eventually periodic synthesis exists. We also consider specific cases, where we show that the synthesis if existent can always be chosen to be of the same eventually periodic class as the plant. All the conditions derived are provided in terms of semi-definite programming problems. The motivation for this work is controlling nonlinear systems along prespecified trajectories, notably those which eventually settle down into periodic orbits and those with uncertain initial states.