Local $L2$ Gain of Axial Flow Compressor Control

Feedback control has been pursued to stabilize the bifurcated operating solution near the rotating stall point in axial-flow compressors. These controllers can extend the stable operating range and hence improve engine performance. However, the local $L2$ gain of these controllers still remains unknown. In this paper, a family of Lyapunov functions is first constructed, and then the local $L2$ gain is derived through Hamilton–Jacobi–Bellman inequality for a class of stabilizing controllers with throttle position as actuator and pressure rise as measurement. The results obtained in this paper provide useful guidance for selecting the most robust controller from a given class of stabilizing controllers in terms of $L2$ gain.