LMI tools for eventually periodic systems

This paper is focused on the concept of an eventually periodic linear discrete-time system. We derive a necessary and su4cient analysis condition for checking open-loop stability and performance of such systems, and use this to derive exact controller synthesis conditions given eventually periodic plants. All the conditions derived are provided in terms of semi-de9nite programming problems. The motivation for this work is controlling nonlinear systems along prespeci9ed trajectories, notably those which eventually settle down into periodic orbits and those with uncertain initial states. c © 2002 Elsevier Science B.V. All rights reserved.