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 stem 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.