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. Both theoretical analysis and numerical examples show that the results in this paper are generally less conservative than those in the quadratic framework. (C) 2009 Elsevier Ltd. All rights reserved.