  We propose a discrete-time integral resonant control (IRC) approach for
negative imaginary (NI) systems, which overcomes several limitations of
continuous-time IRC. We show that a discrete-time IRC has a step-advanced
negative imaginary property. A zero-order hold-sampled NI system can be
asymptotically stabilized using a discrete-time IRC with suitable parameters. A
hardware experiment is conducted where a high-speed flexure-guided
nanopositioner is efficiently damped using the proposed discrete-time IRC with
the discrete-time controller being implemented in FPGA hardware at the sampling
rate of 1.25 MHz.
