Stability analysis of discrete-time systems with quantized feedback and measurements

This paper considers a quantized system with finite-level quantized input computed from quantized measurements (QIQM). The problem of globally asymptotic stability of QIQM system is transferred to the one of an equivalent system depending on a multiplier which is nonnegative and bounded. It is the focus of this paper to discuss the nonnegativity and boundness of the multiplier. A sufficient condition is given for the globally asymptotic stability of QIQM system. Note the main method used here is similar to the one used by Richter and Misawa, in which the uniform quantizer is employed. This paper is the extension of that work to the logarithmic quantization which is more advantage than the uniform one. A numerical simulation is presented at last to show the effectiveness of the main results and the advantage of logarithmic quantization compared to uniform quantization.