Sufficient conditions for the nonoscillation of nonlinear pulse-controlled systems

In this paper, the sufficient conditions for the absence of periodic modes for unforced nonlinear pulse-controlled feedback systems are given. These criteria relate to the behaviour of discrete nonlinear feedback systems within the Popov-Hurwitz sector, and the structurally similar in form to the well known circle and Popov criteria of the frequency domain, with the same simple graphical interpretation. The pulse controllers under consideration are of the pulsewidth or pulse-amplitude type, and a general classification of pulse controllers is given. Illustrative examples of systems that fail the Aizerman and Kalman conjectures are investigated with the techniques developed in the paper to evaluate the largest nonlinearity sector that guarantees the absence of certain periodic modes.