Improved structured filter design and analysis for perturbed phase-locked loops via sector and H∞ norm constraints with convex computations.

This work focuses on designing a structured filter in a phase-locked loop (PLL) system that is perturbed by nonlinear effects from the phase comparator. The filter is designed based on H∞ control synthesis which is also optimized along with the stability condition of the nonlinear PLL model. The improvement on the design technique is introduced via relaxations of the H∞ norm constraint on the system’s frequency response and integration with the nonlinearity’s sector bound. The resulting problems are then formulated into matrix inequalities where the solvability conditions are provided via convex computation approaches. Numerical results and computer simulations demonstrate that the tracking capability of the PLL can be enforced via the proposed methods which then lead to a wider lock-in range and a faster acquisition time as compared to existing techniques.