Stability of positive-position feedback controllers with low-frequency restrictions

Positive-position feedback has been presented as a suitable alternative to the negative-velocity feedback approach taken in active damping applications. This has motivated the application of Negative-Imaginary Systems theory to study the stability of controllers based on positive-position feedback. However, this theory cannot be applied in cases where low-frequency dynamics of the sensors, actuators and/or controllers hinder the application of Negative-Imaginary stability conditions. This work extends the theory of Negative-Imaginary Systems by obtaining simple analytical stability conditions when such low-frequency restrictions are present.