On the absolute stability approach to quantized H_∞ control

The H∞ performance analysis of quantized feedback control systems is revisited in this paper. By applying some intrinsic properties of the logarithmic quantizer and the sector bound conditions, we present a new approach to H_∞ performance analysis of control systems with input quantization. The results are expressed in linear matrix inequalities (LMIs) and are valid for both single-input and multiple-input discrete-time linear systems with logarithmic quantizers. The key point of our method is the utilization of Tsypkin-type Lyapunov functions in the absolute stability analysis problem, rendering generally less conservative results than those in the quadratic framework, which is shown both through theoretical and numerical analysis.