Stabilization of a continuous linear system over channel with network-induced delay and communication constraints

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. Under the channel encoder without access to control inputs, a coding scheme based on spherical polar coordinates is proposed for this problem. Two cases are addressed: (1) in the case that the channel decoder does not utilize control inputs, instead of the original system, the corresponding augmented system is used to estimate the upper and lower bounds of the state norm of the original system for quantization, which simplifies the design of the coding scheme. And a definite relation between the quantized data and the corresponding quantization error is used to present the condition for the stability of the system; (2) in the case that the decoder utilizes control inputs, instead of quantizing the system state at each time step as usual, the encoder quantizes the initial state all the time by updating the parameters of the quantizer, which also simplifies the design of the coding scheme. Sufficient conditions guaranteeing that the system is stable are presented for the two cases, respectively, and the corresponding design methods for coding schemes are given.