Performance Control of Linear Systems Using Quantized Feedback

This paper studies two control problems for linear systems using quantized feedback, namely quadratic performance control and H∞control. We first revisit the work by Elia and Mitter on quadratic stabilization of linear systems using quantized state feedback with a logarithmic quantizer. We reinterpret their result on coarsest quantization density using a sector bounded method. This allows us to generalize their work to the aforementioned performance control problems. We give conditions under which a given quantization density yields a linear controller that guarantees a required level of performance.