Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems

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 (P I I2 RC) and a HIGS-based PII2 RC, and we show that both of them can be applied to asymptotically stabilize an NI system. An example is provided to illustrate the proposed results.