Self-triggered Stabilization of Contracting Systems under Quantization

We propose self-triggered control schemes for nonlinear systems with quantized state measurements. Our focus lies on scenarios where both the controller and the self-triggering mechanism receive only the quantized state at each sampling time. We assume that the ideal closed-loop system without quantization or self-triggered sampling is contracting. Moreover, an upper bound on the growth rate of the open-loop system is assumed to be known. We present two control schemes that achieve closed-loop stability without Zeno behavior. The first scheme is implemented under logarithmic quantization and uses the quantized state for the threshold in the triggering condition. The second one is a joint design of zooming quantization and self-triggered sampling, where the adjustable zoom parameter for quantization changes based on inter-sampling times and is also used for the threshold of self-triggered sampling. In both schemes, the self-triggering mechanism predicts the future state from the quantized data for the computation of the next sampling time. We employ a trajectory-based approach for stability analysis, where contraction theory plays a key role.