Absolute stability of a class of nonlinear sampled-data systems

The present investigation studies the problem of absolute stability of a class of nonlinear sampled-data control systems with or without integrators in the loop. An absolute-stability criterion has been obtained by the second method of Lyapunov. The same stability criterion has been derived previously by the authors via the Popov approach. The criterion is shown to be a sufficient condition for the existence of a certain type of Lyapunov function which assures global-asymptotic stability of the class of systems under investigation. In contrast to previous results, the criterion does not place any restriction on the number of integrators in the loop. A systematic step-by-step method for applying the inequality is given, and an example illustrating the application of this frequency-domain inequality and a comparison with previous results are presented. The method is found to be versatile and more effective, and, in general, a better stability boundary can be obtained.