Multi-objective LPV L2-gain control with game-theoretic synthesis

It was proved that the DGKF H∞-control is still an observer-based control, but the embedded Kalman-filtering has been calibrated by the maximum disturber from the Nash-game perspective. Following such a game-theoretic synthesis, this paper furthers the DGKF H∞-control for quadratic regulation of multiple L2-gain objectives, which is beyond the capability of the mainstreamed syntheses that counts mostly on sophisticate LMIs algebra. Two aspects of improvement are made: (1) instead of assuming Kalman-filtering, the feasible set of Luenberger gains is formulated into LMIs by a slack variable to remove structural conservatism; and (2) in case of LPV systems, a finite-element method is provided for numerically solving the differential LMIs therefrom.