Elimination of Overflow Oscillations in Nonlinear Discrete Time State Delayed Systems in the Presence of External Disturbance

Abstract

The processing of signals is desired to be linear operations in many applications. However, signal processing in discrete-time systems with finite wordlength implies that linearity can be reached to a certain level and deviation from the linear operation can be minimized by selecting longer wordlength. Yet there may be finite wordlength effects due to which nonlinearities may occur that drive the linear discrete-time systems into nonlinear discrete-time systems. An essential issue in the field of nonlinear systems is the qualitative analysis, especially the stability analysis. In this research work, a particular class of nonlinear systems, digital filters with overflow nonlinearities are considered to investigate their stability properties. newlineDigital filter is a discrete system that works according to a designed algorithm to modify certain parameters of discrete signals. Digital filters are invariably subject to non-idealities derived from their infinite precision arithmetic. Nonlinearities such as overflow and quantization are generated in digital filters due to the finite wordlength realization. The presence of nonlinearities may produces zero-input limit-cycles and causes the realized system to become unstable. The presence of time-delays in the digital filters is another source for instability. The delays generally appear due to transport lags, measurement lags and signal transmission with finite speeds. On another research front, it has been recognized that systems performance may be degraded in the presence of external disturbance. The disturbance may be encountered in the higher-order digital filters when implemented using the lower-order digital filters to prevent finite wordlength effects. So, considering combined effects of nonlinearities, delay and external disturbance, it is necessary to have sophisticated algorithms or rules to select the system coefficients so that the designed filter is stable and free from limit-cycles.