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Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems (2403.15140v2)

Published 22 Mar 2024 in eess.SY, cs.SY, and math.OC

Abstract: 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.

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