$\mathcal {H}_\infty$/LTR-Based Synthesis of Multivariable 2-Rate Dynamic Output Feedback Control With Some Applications

Aiming to provide better compensation to discrete-time (or, sampled-data), multivariable, linear time-invariant (LTI) plants that have nonminimum phase zeros, this article proposes a 2-rate, 2-degree-of-freedom, dynamic output feedback controller. Employing the lifting technique that may convert a 2-periodic system to a time-invariant form, it is shown that, under certain conditions, the equivalent LTI plant becomes a minimum-phase one. Consequently, an
$\mathcal {H}_\infty$
/loop-transfer-recovery-based LTI approach is used to compensate the same in respect of both robustness and response. Several examples are presented to show that the proposed 2-rate compensation may provide 1) superior robustness against plant parameter variations, 2) improved quantized control, and 3) detection and mitigation of zero-dynamics attack (ZDA) in cyber-physical systems (CPSs).