Periodic oscillations and relative stability of discrete dynamical systems on integer grid coordinates

Abstract

In the digital society, information, communication and control technologies are realized based on a packet of signals (or a finite number of data). That is, control systems are operated by discretized/quantized signals not only in the time domain but also in the spatial domain (state space). In this paper, the stability of such (nonlinear) discrete dynamical systems is analyzed based on multiple metrics and simultaneous linear inequalities on integer grid (lattice) coordinates. Numerical examples for a 3rd order discrete feedback system with saturation-type and inclined wave-type nonlinearities are presented to clarify the meaning of the relative stability and the existence of various periodic oscillations. In these examples, it can be found that there exist different limit-cycles and furthermore limit-cycles with different (longer) period.