  A hybrid integrator-gain system (HIGS) is a control element that switches
between an integrator and a gain, which overcomes some inherent limitations of
linear controllers. In this paper, we consider using discrete-time HIGS
controllers for the digital control of negative imaginary (NI) systems. We show
that the discrete-time HIGS themselves are step-advanced negative imaginary
systems. For a minimal linear NI system, there always exists a HIGS controller
that can asymptotically stablize it. An illustrative example is provided, where
we use the proposed HIGS control method to stabilize a discrete-time
mass-spring system.
