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Current systems such as: satellites, aircrafts, automobiles, turbines, power controls and traffic controls are becoming increasingly complex and/or highly integrated as prescribed by the SAE-ARP-4754 Standard. Such systems and their control systems use many modes of operation and many forms of redundancy to achieve high levels of performance and high levels of reliability under changing environments and phases of their lifecycle. The environment disturbances, environment variability, plant non-linear dynamics, plant wear, plant faults, or the non-symmetric plant operation may cause de-synchronization in phase or time among: 1) simultaneous units in the same normal mode of operation; 2) successive units in successive normal modes of operation; 3) main and spare units from normal to faulty modes of operation. So, techniques to reduce those causes or their effects are becoming important aspects to consider in the design of such systems.

Current systems such as satellites, aircrafts, automobiles, turbines, wind power generators and traffic controls are becoming increasingly complex and/or highly integrated as prescribed by the SAE-ARP-4754 Standard. Such systems frequently require accurate generation, distribution and time or phase synchronization of signals with different frequencies that may be based on one reference signal and frequency. But the environment fluctuations or the non-linear dynamics of these operations cause uncertainties (skew and jitter) in the phase or time of the reference signal and its derived signals. So, techniques to reduce those causes or their effects are becoming important aspects to consider in the design of such systems. The PLL techniques are useful for establishing coherent phase or time references, jitter reduction, skew suppression, frequency synthesis, and clock recovery in numerous systems such as communication, wireless systems, digital circuits, rotors, and others.