On the absolute stability approach to quantized feedback control: Further insight

By exploring some geometric properties of the logarithmic quantizer and using the fact that the logarithmic quantizer is sector bounded and nondecreasing, this paper presents a new approach to the stability analysis of quantized feedback control systems. Our method is based on Tsypkin-type Lyapunov functions that have been widely used in absolute stability analysis problems. The results are expressed in linear matrix inequalities (LMIs) and are valid for both single-input and multiple-input discrete-time linear systems with a logarithmic quantizer. Theoretical analysis shows that the results in this paper are generally less conservative than those in the quadratic framework.