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Dirty derivatives are routinely used in industrial settings, particularly inthe implementation of the derivative term in PID control, and are especiallyappealing due to their noise-attenuation and model-free characteristics. Inthis paper, we provide a Lyapunov-based proof for the stability of lineartime-invariant control systems in controller canonical form when utilizingdirty derivatives in place of observers for the purpose of output feedback.This is, to the best of the authors' knowledge, the first time that stabilityproofs are provided for the use of dirty derivatives in lieu of derivatives ofdifferent orders. In the spirit of adaptive control, we also show how dirtyderivatives can be used for output feedback control when the control gain isunknown.

Dirty derivatives for output feedback stabilization