On the stability of pulse-width-modulated feedback systems

The objective of this paper is to present a frequency-domain stability criterion for pulse-width-modulated feedback systems. The criterion states that 1) if the Nyquist locus of the pulse transfer function of the linear plant does not intersect or encircle a certain disk in the complex plane, then the system is l
2
bounded input-bounded output stable, and 2) if the impulse response of the linear plant is zero at
t = 0
, then the radius of the disk approaches zero as the ratio of the linear-plant bandwidth to the pulse-width-modulator frequency approaches zero. It is shown that the result in 2) implies that the criterion in 1) essentially becomes the well-known Nyquist criterion for sample-data systems when the pulse-width-modulator frequency is sufficiently large. This result permits the use of the standard design techniques for linear sample-data systems in a wide class of pulse-width-modulated systems. Consequently the design of these systems can be greatly simplified.