On the stability of a certain class of nonlinear sampled-data systems

A sufficient condition for stability of a class of sampled-data feedback systems containing a memory-less, nonlinear gain element is obtained. The new stability theorem for the class of systems discussed requires that the following relationship be satisfied on the unit circle: . In this papers the stability criterion embodied in this theorem can be readily obtained from the frequency response of the linear plant. This method is essentially similar to Popov\´s method applied to the study of nonlinear continuous systems. Furthermore, Tsypkin\´s resuits for the discrete case are obtained as a special case when . Several examples are discussed, and the results are compared with Lyapunov\´s quadratic and quadratic plus integral forms as well as with other methods. For these examples, the results obtained from the new theorem yield less conservative values of gain than Lyapunov\´s method. Furthermore, for certain linear plants the new theorem also yields the necessary and sufficient conditions.