Stabilize an n-dimensional quantized nonlinear feedforward system with 1 bit

Abstract

This paper studies the stabilizability of an n-dimensional quantized feedforward nonlinear system. The state of that system is first quantized into a finite number of bits, then sent through a digital network to the controller. In order to save network bandwidth, people pursue as less quantization bits as possible to maintain stability of such a system. In DePersis' paper [1], n bits are used to stabilize the n-dimensional system by assigning one bit for each state variable (dimension). This paper extends that result by stabilizing the whole system with a single bit under the same assumptions. Its key contribution is a dynamic quantization policy which dynamically assigns the single bit to the most "important" state variable. Under this policy, the quantization error exponentially converges to 0 and the asymptotic stability of the system can, therefore, be guaranteed. Because 1 bit is the smallest bit number in each packet, the new policy achieves the minimum stabilizable bit number for that n-dimensional feedforward nonlinear system. ©2009 IEEE.