Further Results on Periodically Time-Varying Dynamical State-Feedback Controller Synthesis for Discrete-Time Linear Systems

In this paper, we enhance the quality of our preceding results on periodically time-varying dynamical state-feedback controller (PTVDSFC) synthesis for discrete-time linear periodic/time-invariant systems. We firstly revisit PTVDSFC synthesis for uncertainty-free systems and derive necessary and sufficient LMI conditions for the existence of the desired PTVDSFCs. Based on these LMIs, we next consider robust H∞-PTVDSFC synthesis for polytopic-type uncertain systems and demonstrate that we can indeed obtain less conservative results. We finally derive a viable test to verify that the designed robust PTVDSFC is “exact” in the sense that it attains the best achievable robust H∞ performance. This exactness verification test works fine in practice, and we show via numerical examples that exact robust control is indeed possible via PTVDSFC, even for those problems where the standard static state-feedback fails.

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