Robust stability analysis of discretized nonlinear control systems

This paper describes a robust stability analysis of discrete-time and discrete-value (discretized/quantized) nonlinear control systems in a frequency domain. First, by considering a threshold in the input of nonlinearity, the discretized nonlinear characteristic in a grid pattern is partitioned into two parts: a bounded area under the threshold and a sectorial area defined over the threshold. Then, allowing a fluctuation or an off-set in the bounded area, the concept of the robust stability for discrete-time systems, which was developed in the previous papers, is applied to this type of nonlinear control system. In this paper, in order to relax the restriction of the assumptions in the previous papers, a new technique for discretizing is proposed. As a result, a robust stability condition in a global sense is given, and the stabilization of discretized nonlinear control systems can be realized.