Comparison of stability criteria for interconnected systems with pulse frequency modulation

Stability criteria for systems containing an arbitrary number of pulse frequency modulators are considered, which fall under three basic categories, namely, Lyapunov's second method, frequency domain method, and a direct method for global finite pulse stability (GFPS) introduced earlier by the authors. The criteria are compared with respect to effectiveness (in terms of size of [parameter-] region sufficient for stability), generality (in terms of classes of applicable systems), and ease of application. The direct GFPS criterion is the simplest to apply and, at the same time, provides bounds on the number of pulses emitted by each modulator. Comparative examples yielded greater stability regions (of parameters) from the direct GFPS criterion than from (optimal application of) a recent frequency domain criterion of Gelig. A criterion based on Lyapunov's second method could provide good stability regions, but it is most difficult to apply, especially, for higher order systems.