非线性系统的右独立阶及其应用

定义非线性右可逆系统的一组结构常量, 即右独立阶. 证明右独立阶在正则静态反馈下保持不变,同时举例指出右独立阶在正则动态反馈下可以改变. 研究了右独立阶在解耦问题中的应用, 指出利用右独立阶可完全刻划正则静态反馈解耦问题,并初步讨论了右独立阶在非线性Morgan问题上的应用.

Right Essential Orders of Nonlinear Systems and its Application

A new set of invariants was defined for right invertible nonlinear control systems,the right essential orders. We prove that this set of natural numbers is invariant under regular static state feedbacks. On the other hand, it is pointed by an example that the right essential orders are changeable by regular dynamic state feedbacks. Some application of the right essential orders to the decoupling problem is addressed. Especially, a new necessary and sufficient condition is obtained via the right essential orders for the regular feedback decoupling problem of nonlinear systems. The relation between the right essential orders and the nonlinear Morgan's problem is also discussed. It is expected that the invariants introduced here plays an important role in the study of nonlinear Morgan's problem.