On Gain-Scheduled State-Feedback Controller Synthesis with Quadratic Stability Condition

This letter shows that, as long as continuous-time linear parameter-varying (LPV) systems are concerned, quadratic-stability-based gain-scheduled state-feedback controller synthesis offers no advantage over quadratic-stability-based fixed (parameter-independent) state-feedback controller synthesis in typical control performance specifications. We derive this counterintuitive result by properly extending the previous results on the robust versions of Finsler's lemma and the elimination lemma. We also show that this counterintuitive result is continuous-time LPV system specific, and in the discrete-time LPV system case quadratic-stability-based gain-scheduled state-feedback controller synthesis does bring improvement. These results give a proper warning about the effectiveness of the quadratic-stability-based gain-scheduled state-feedback controller synthesis.