Stability analysis of a class of nonlinear multirate digital control systems

We consider multirate digital control systems which consist of an interconnection of a continuous-time nonlinear plant (described by ordinary differential equations) and a digital lifted controller (described by ordinary difference equations). The input to the digital controller consists of the multirate sampled output of the plant and the input to the continuous-time plant consists of the multirate hold output of the digital controller. We show that when quantizer nonlinearities are neglected, then under reasonable conditions (which exclude the critical cases), the stability properties (in the Lyapunov sense) of the trivial solution of the nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization. When quantizer nonlinearities are not neglected, corresponding results can be established for Lagrange stability rather than Lyapunov stability of an equilibrium.