Lagrange Stability of Quantized State Feedback Control Systems via Binary-expansion

Abstract

In this paper, we consider the problem of stabilizing the state feedback control systems that have quantizers in feedback loop. We study “the binary expansion quantization” where by using the finite bits measurement signals are endorded. Since there is no assumption on the infinite fineness of the quantizer, asymptotic stability cannot be ensured. However we derive a sufficient condition, in terms of the matrix norm and the matrix inequality form, on a quantization bit rate and gains for the ultimate boundedness of the state of the closed loop.