Stability Analysis of High-Resolution Quantized Feedback Systems

In this paper, we study the stability of a high resolution quantized feedback system. It is well known that a quantized feedback system can be stabilised by increasing the resolution of the quantizer. However, limit cycles have also been found under certain conditions at high resolution. These necessary and sufficient conditions for the existence of limit cycles are examined. Solutions for the limit cycle period and switching instants obtained via the inverse-free Newton's method are used to assess the stability of the limit cycle under high resolution with the Poincaré map. A bound on the quantization resolution is identified for a stable limit cycle. Analytical results on the existence of limit cycles in first and second order systems are also presented.