The Complete Analysis of Feedback Capability for Polynomial Uncertain Systems

We consider the capability of feedback for a class of polynomial nonlinear systems with both unknown parameters and bounded noises. In the single parameter case, Li, C. and Xie, L. (2006) demonstrated that the necessary and sufficient condition for the existence of a feedback stabilizer is that the nonlinear growth rate of the system dynamics is less than 4. In the multiple parameter case, the necessary and sufficient condition turns out to be governed by a polynomial rule, which is identical to the necessity condition obtained in Xie, L.L. and L. Guo (1999) for the Gaussian white noise case. This paper complete the analysis of the feedback capability criterion stated in Li, C. et al. (2005) by providing the necessity proof of the polynomial rule.