Mixed H_∞/H₂ design of digital phase locked loops with polytopic type uncertainties

A robust H_∞ control method is applied to the design of loop filters for digital phase locked loop carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and with a significant decision delay in the closed loop that may stems from the decoder and/or the equalizer there. The design problem is transformed into a state-feedback control problem where phase and gain margins should be guaranteed in spite of the uncertainty. Of all the loop filters that achieve the required margins the one that minimizes an upper-bound on the effect of the phase and the measurement noise signals is derived.