Quantized feedback stabilization of non-linear affine systems

Recently, the study of quantized control systems has attracted increasing attention from researchers, due to its theoretical and practical importance in digit control, control under communication/computation constraints, etc. In this paper we develop a theory of stabilizing single-input non-linear affine systems using quantized feedback. We construct explicitly a stabilizing quantizer based on a control Lyapunov function (CLF), and a robustly stabilizing quantizer based on a robust control Lyapunov function (RCLF). We characterize the coarsest quantizer for a given RCLF and the coarsest one over all RCLFs. The special features of several classes of non-linear affine systems are explored to obtain more specific results. Finally, we apply the proposed quantization scheme to the motion control of certain types of vehicles.