Quantized Feedback Stabilization of System With Network-Induced Delay

This paper considers the stabilization problem of a continuous linear system over a communication channel with network-induced delay. The channel is of finite data rate and connects the measurement sensor to the controller. Based on spherical polar coordinates, a novel coding scheme is proposed for this problem. In this coding scheme, the quantizer does not quantize the state of the original quantized system directly, but quantizes the state of the corresponding augmented system to produce control inputs, which simplifies the design of the coding scheme; a definite relation between the quantized data and the corresponding quantization error is used to facilitate the analysis of the stability of the system. Based on this coding scheme, the paper presents the condition guaranteeing the asymptotic stability of the system with network-induced delay and gives the design procedure of quantizer and controller. It is shown that adopting spherical polar coordinates makes the practical solving for the parameters of the quantizer and the controller numerically realistic.