Discrete signals, feedback and oscillation

The problem of feedback and oscillation in animals and machines was once presented by N. Wiener. Since then, the dynames of automatic (feedback) control and recent robotic systems has been examined based on this concept. In this paper, the stability of discrete (discrete-time and discrete-value) feedback systems is considered adapting to the computerized age. The stability condition of (nonlinear) discrete systems is derived by using the extended small-gain-theorem with an arbitrary number q. The relationships between this condition and Popov´s criterion and Aizerman´s conjecture in continuous signals are discussed. In numerical examples, some discrete time-responses and chaotic oscillations are shown in relation to the size of sampling-period and the magnitude of step-input.