The convergence of a PLL with variable parameters
A phase-locked loop with variable parameters is considered. In such a system it is possible to obtain a short convergence time together with a small bandwidth. It is supposed that the PLL's parameters cannot be switched and there is a restriction on the velocity of the parameter variation. 
 
 
 
An optimal strategy of parameter variation is obtained which gives an improvement in convergence time by a factor of about 30 in comparision to fixed parameter and small-bandwidth PLLs.
Optimum phase-acquisition technique for charge-pump PLL
In this paper, we propose a new optimum phase-acquisition algorithm controlling the loop gain of a charge-pump PLL (CP-PLL) in the sense of the MMSE criterion. A set of recursive difference equations minimizing RMS jitter of output phase is derived to obtain an optimum gear-shifting sequence with a zero-phase start (ZPS) assumption. It is shown that the optimum gear-shifting sequence is independent of the variance of the input phase jitter. A procedure for applying this sequence to the design of CP-PLL circuits is described, Both behavoral simulation and HSPICE circuit-level simulation demonstrate that the proposed design leads to an efficient CP-PLL having both fast acquisition and significant jitter reduction characteristics. The optimal gear-shifting CP-PLL outperforms the conventional CP-PLLs. These methods can be used for clock recovery applications such as data communication receivers, disk drive read/write channels, and local area networks, as well as for other applications requiring very short initial preamble periods.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.