Communications in Information and Systems

Volume 6 (2006)

Number 4

A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems

Pages: 273 – 298



Lei Guo

Chanying Li

Liang-Liang Xie


In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyzes of the stabizability condition, which is determined by the growth rates of the system nonlinear dynamics only.


Uncertain nonlinear systems, Adaptive control, Robust stability, Discrete-time systems, Feedback capability

Published 1 January 2006