Safe Digital Stabilization of Nonlinear Systems with an Application to Glucose Control

In this paper, we propose a framework for the semiglobal practical safe stabilization of nonlinear continuous-time systems based on limited amount of information. This approach requires the availability of a continuous-time control law ensuring global asymptotic stability and a robust safety condition. Following an emulation-based approach, we introduce time sampling and quantizations on the input and state signals. We show that sufficiently high sampling frequency and small quantization error guarantee safety preservation and practical state stabilization to an arbitrarily small neighborhood of the origin while keeping the state within a safe region during the whole system evolution, which is essential in safety-critical applications. Numerical simulations on a glucose control problem in a non-ideal setting show the effectiveness of the approach.