Stability of continuous-time nonlinear systems with digital controllers

This paper is concerned with a gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances on both input and output channels. The principal idea is to design a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap between the two controllers. It is expected that, under general conditions, the computed gap depends on the discrete sample size and the faster the sample rate, the smaller the gap and, therefore, the existing gap metric robust stability theorems can be applied to obtain both stability and performance results for an appropriately discretised controller. This is shown for the case of memoryless controllers and for a more general class of controllers specified by stable, causal operators. In both cases, the controllers are required to be incrementally stable.