Phase-controlled system design via mixed H∞ synthesis and nonlinear method

Due to nonlinear behavior of several phase-detectors, linear approximation method often leads to performance degradation in many phase-controlled systems, particularly when the phase errors are sufficiently large. In this work, with the nonlinearity considered in the system's model, a suitable criterion which takes into account both the nonlinearity's sector and slope bounds is employed to establish its global stability condition. The result is then incorporated into the existing H∞ synthesis in the controller/loop filter design. The searches are expressed in terms of convex linear matrix inequalities which are computationally tractable. To illustrate the improvement introduced via this approach, several numerical examples are included with comparisons over conventional linear approximation methods.