Exponential stability of controllers using reduced order actuator and system models with residual mode filters

Control of systems described by large-order models typically requires construction and use of reduced order models (ROMs) for the purpose of feedback controller design and implementation. However, controllers based on these ROMs can have deleterious interactions with unmodeled modes, and some sort of stability compensation is needed, such as residual mode filters (RMFs). We prove that exponential closed loop stability using RMFs can be achieved for reduced order systems with actuators, as well as for controllers designed using only a ROM of the actuator