Finite-Level Quantized Feedback Control for Linear Systems

Studies have shown that a logarithmic quantizer can provide the coarsest quantization for quadratic stabilization of linear systems using quantized feedback. However, the coarsest quantizer has an infinite number of quantization levels, which is not implemented in practice. In this paper, we investigate the quantized feedback control problem for discrete-time linear systems using a finite-level logarithmic quantizer. We introduce a dynamic scaling method for the logarithmic quantizer and show that asymptotic stabilization can be achieved with a moderate number of quantization levels. Our approach is easily implemented. We also study the quantized feedback stabilization problem for systems with bounded stochastic noise inputs and show that the system state can converge to a bounded region using a finite-level logarithmic quantizer in conjunction with a proper dynamic scaling scheme