The effect of discretized feedback in a closed loop system

When a continuous time control law is implemented using a digital computer, the closed loop system may not have the same stability properties as the system with a true continuous controller due to delay and digitization errors. Using a Lyapunov analysis, this paper shows that, for linear systems and a class of nonlinear systems with discretized feedback, some stability properties can be preserved if the sampling frequency is properly chosen. In particular, we propose a variable sampling interval scheme for linear systems. This scheme is desirable when (1) computer resources are tightly shared by many tasks or (2) power consumption is critical. The effect of truncation error is also studied.