A stability criterion for pulse-width-modulated feedback control systems

Aizerman's method for investigating asymptotic stability in the large, which was extended by Kodama to encompass nonlinear sampled-data systems, is further extended in this paper. The concept is developed with specific reference to pulse-width-modulated feedback systems, but the method is applicable to a more general class of nonlinear discrete-time systems. The significant difference between the class of systems treated here and the class treated by Kodama is that in the latter class the nonlinear factor is a scalar, whereas in the former, it is a vector. This difference is not trivial; the presence of the vector nonlinearity requires a substantial change in the procedure for determining the range of a parameter over which the system is asymptotically stable in the large. By application of the method presented in this paper, one can obtain a sufficient condition for asymptotic stability in the large of pulse-width-modulated feedback systems. The method is not limited to cases in which the poles of the transfer function of the plant are real and/or simple and the result obtained, at least in those cases investigated to date, is not highly conservative.