Generalized Stability Triangle and Robust Phase Compensator Design The primary objective of this paper is to design a secondorder recursive allpass digital phase compensator with arbitrarily predetermined stability robustness. The resulting phase compensator has robust stability, and thus can avoid the possible instability that may be caused by the perturbations of system coefficients. To achieve a predefined stability robustness, the generalized stability triangle (GST) proposed by the author is adopted to the design process. Furthermore, the utilization of the GST requires coefficient conversions that convert the original unconstrained compensator coefficients to the functions of new design variables, and then the optimum values of the new variables are found. A demonstrative design is illustrated to show the effectiveness of the GSTbased design method as well as the stability robustness of the resultant biquadratic phase compensator.

Improved structured filter design and analysis for perturbed phaselocked loops via sector and Hxe2x88x9e norm constraints with convex computations Abstract   This work focuses on designing a structured filter in a phaselocked loop (PLL) system that is perturbed by nonlinear effects from the phase comparator. The filter is designed based on     H  xe2x88x9e     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  xe2x88x9e     norm constraint on the systemxe2x80x99s frequency response and integration with the nonlinearityxe2x80x99s 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 lockin range and a faster acquisition time as compared to existing techniques.