Robust stability analysis for discretized nonlinear control systems in a global sense

This paper describes the robust stability analysis for discrete-time and discrete-value (discretized/quantized) nonlinear control systems in a frequency domain. First, by considering an appropriate threshold in the input of nonlinearity, the discretized (stepwise) nonlinear characteristic on a grid pattern is partitioned into two sections: a bounded area that is defined under the threshold and a sectorial area that is defined over the threshold. Then, allowing for a fluctuation or an offset in the bounded area, the concept of robust stability for nonlinear discrete-time systems, which was developed in the previous studies, is applied to this type of a closed loop system. As a result, the stability problem of discretized nonlinear control systems is elucidated, and a robust stability condition in a global sense is derived. Numerical examples are shown to verify the result