Invariant set analysis for discrete-time polynomial nonlinear feedback systems with dynamic quantizers

This paper deals with invariant set analysis for discrete-time polynomial nonlinear feedback single input and single output systems with dynamic quantizers where the control input signal takes discrete values. The paper starts with invariant set analysis for discrete-time polynomial nonlinear systems with bounded disturbances. Since the quantization error is also bounded, analysis of feedback systems including the dynamic quantizers can be reduced to invariant set analysis. Some sufficient conditions for analysis are obtained that can be solved by numerical optimization. Examples illustrate upper bounds of a cost function based on the proposed analysis method.