  We introduce a hybrid control system called a hybrid integrator-gain system
(HIGS) based integral resonant controller (IRC) to stabilize negative imaginary
(NI) systems. A HIGS-based IRC has a similar structure to an IRC, with the
integrator replaced by a HIGS. We show that a HIGS-based IRC is an NI system.
Also, for a SISO NI system with a minimal realization, we show there exists a
HIGS-based IRC such that their closed-loop interconnection is asymptotically
stable. Also, we propose a proportional-integral-double-integral resonant
controller and a HIGS-based proportional-integral-double-integral resonant
controller and show that both of them can be applied to asymptotically
stabilize an NI system. An example is provided to illustrate the proposed
results.
