Quantized state feedback stabilization with signal-to-noise ratio constraints

This paper deals with the problem of state feedback stabilization for single-input discrete-time systems over a communication channel, where both logarithmic quantization error and white noise are included. The logarithmic quantizer is characterized by a received signal-to-error ratio (R-SER) model and the white noise is modelled by additive white Gaussian noise (AWGN) channel where a signal-to-noise constraint is imposed. The desired control law is aimed to stabilize the system in the presence of quantized error and to satisfy some pre-specified power constraint, simultaneously. A solvability condition is derived in terms of Mahler measure of the plant and the desired feedback controller is obtained through solving an algebraic Riccati equation. An example is included to illustrate the current results.