Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems

This is a continuation of our preceding study dealing with robust stabilizing controller synthesis for uncertain discrete-time linear periodic/time-invariant systems. In this preceding study, we dealt with the case where the underlying systems are affected by polytopic-type uncertainties and revealed a particular periodically time-varying dynamical controller (PTVDC) structure that allows LMI-based robust stabilizing controller synthesis. Based on these preliminary results, in this paper, we provide LMI conditions for robust H₂ and H_¿ PTVDC synthesis. One of the salient features of the proposed method is that we can reduce the conservatism and improve the control performance gradually by increasing the period of the controller to be designed. In addition, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we illustrate that our design method is indeed effective to achieve less conservative results under both the periodic and time-invariant settings.