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

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