Some qualitative properties of multirate digital control systems

The authors consider multirate digital control systems which consist of an interconnection of a continuous-time nonlinear plant (described by ordinary differential equations), a digital controller (described by ordinary diffe rence equations) which has quantizers (but is otherwise linear), along with the required interface elements (A/D and D/A converters). The input to the digital controller consists of the multirate sampled output of the plant. In the present paper, the authors show that when quantizer nonlinearities a re neglected, then under reasonable conditions (which exclude the critical cases), the stability properties (in the Lyapunov sense) of the trivial sol ution of a nonlinear multirate digital control system can be deduced from t he stability properties of the trivial solution of its linearization, For s uch systems we also present a result concerning the existence and construct ion of stabilizing multirate-output digital controllers. In the present paper, the authors also show that the solutions of a multira te digital feedback control system with nonlinear plant and quantizers are uniformly ultimately bounded if the trivial solution of the corresponding l inear system consisting of the linearization of the plant and with the quan tization removed from the digital controller is asymptotically stable, We a lso provide a result which compares the response of multirate digital contr ol systems with nonlinear plant and quantizers in the controller with the r esponse of the corresponding nonlinear multirate digital control systems wi thout quantizers in the digital controller.