Almost global stability of phase-locked loops

Many control systems have a global dynamical behavior that in addition to a desired stable equilibrium has one or more unstable equilibria or other exceptional trajectories. Typical examples of such systems are pendulums or so called phase locked loops. The objective of the paper is to compare two different methods for analysis of the global behavior in such systems. The first method is LaSalle's invariant set theorem (1967). The second method is the criterion for almost global stability introduced by the author (2001).