论文标题
一类非线性系统的负虚态反馈等效性
Negative Imaginary State Feedback Equivalence for a Class of Nonlinear Systems
论文作者
论文摘要
在本文中，我们调查了一类非线性系统的必要条件，其状态反馈等同于具有正定存储功能的非线性负虚拟（NI）系统。非线性感兴趣系统的相对程度的正常形式小于或等于两个。系统的非线性受到状态变量的子集的限制，该状态变量是具有外部动力学的状态变量。在轻度的假设下，当且仅当它们是弱最小阶段时，这种系统是等于非线性NI系统的状态反馈，而非线性输出严格构成假想（OSNI）系统。这种状态反馈控制方法还可以渐近地稳定有关非线性OSNI系统不确定性的系统。提供了一个数值示例，以显示状态反馈等效控制和不确定系统的稳定的过程。
In this paper, we investigate the necessary and sufficient conditions under which a class of nonlinear systems are state feedback equivalent to nonlinear negative imaginary (NI) systems with positive definite storage functions. The nonlinear systems of interest have a normal form of relative degree less than or equal to two. The nonlinearity of the system is restricted with respect to a subset of the state variables, which are the state variables that have external dynamics. Under mild assumptions, such systems are state feedback equivalent to nonlinear NI systems and nonlinear output strictly negative imaginary (OSNI) systems if and only if they are weakly minimum phase. Such a state feedback control approach can also asymptotically stabilize the systems in question against nonlinear OSNI system uncertainties. A numerical example is provided to show the process of the state feedback equivalence control and stabilization of uncertain systems.
