A Generalized Chordal Metric in Control Theory Making Strong Stabilizability a Robust Property

An abstract chordal metric is defined on linear control systems described by their transfer functions. Analogous to a previous result due to Partington (Linear Operators and Linear Systems. An Analytical Approach to Control Theory. London Mathematical Society Student Texts, vol. 60, Cambridge University Press, Cambridge, 2004) for $H^infty $ , it is shown that strong stabilizability is a robust property in this metric.