单参数离散时间非线性系统的可镇定性定理（英文）

Stabilizability theorem of discrete-time nonlinear systems with scalar parameters

本文对基本的离散时间非线性单参数随机系统建立了可镇定性定理.该定理推进了文献[1]的结果,进一步完善了关于离散时间自适应控制的反馈能力刻画.离散时间单参数系统可镇定的一个重要非线性临界常数是4,用以刻画关于幂函数类系统的反馈能力.而作为本文定理的应用,本文对一类典型的单参数离散时间非线性随机系统发现了新的可镇定临界常数2.

This paper advances [1] by deducing a stabilizability theorem for discrete-time nonlinear systems with scalar parameters, which takes a step forward to the complete characterization of feedback limitations in discrete-time adaptive nonlinear control. It is well-known that exponent 4 is an important critical number to characterize the feedback capability for the basic discrete-time scalar-parameter systems, which are governed by power functions. As an application of our theorem, a new critical number 2 is derived for a typical class of discrete-time nonlinear stochastic systems with scalar parameters.