Limitations in Filtering Structural Vibrations for Unstable Missiles Control

In many problems involving unstable missiles with lightly damped structural modes it might be infeasible to actively dampen structural vibrations due to actuation limitations and/or modeling uncertainty. A common engineering practice in such situations is to use band-stop filters to reduce the effect of vibrations on autopilot feedback loops, known as the mode cancellation approach. This work analyzes the conflict of this strategy with the minimum bandwidth required for stabilization and studies its intrinsic limitations. Namely, we cast the problem as an H
_∞
optimization problem and derive a closed-form criterion for its feasibility. This, in turn, facilitates the formulation of engineering guidelines, which may be useful in preliminary design of agile missiles.