Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems
<|reference_start|>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 and a HIGS-based proportional-integral-double-integral resonant controller, 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.<|reference_end|>
@article{shi2024hybrid,
    title={Hybrid integrator-gain system based integral resonant controllers for
  negative imaginary systems},
    author={Kanghong Shi, Ian R. Petersen},
    journal={arXiv preprint arXiv:2403.15140},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15140},
    primaryClass={eess.SY cs.SY math.OC}
}