论文标题
非线性系统的负假想系统理论：耗散性方法
Negative Imaginary Systems Theory for Nonlinear Systems: A Dissipativity Approach
论文作者
论文摘要
负模糊（NI）系统理论是一个完善的系统理论框架，用于分析和设计线性 - 直变（LTI）控制系统。在本文中，我们旨在将负面虚构系统理论推广到一类非线性系统。基于LTI系统的NI属性的时间域解释，使用适当的工作率的耗散性的形式定义将用于定义一般非线性系统的非线性负虚拟（NNI）属性。根据该新定义，具有力执行器和位置传感器的机械系统是非线性负虚构的。使用Lyapunov稳定性理论，我们试图建立NNI系统正反馈互连NI稳定性结果的非线性概括。将提出具有力为输入的输入和输出的非线性质量 - 弹簧 - 抑制系统的示例，以说明NNI稳定性结果的适用性。此外，将根据NNI系统的耗散框架在非线性域中研究具有自由运动的NI系统的情况。
Negative imaginary (NI) systems theory is a well-established system theoretic framework for analysis and design of linear-time-invariant (LTI) control systems. In this paper, we aim to generalize negative imaginary systems theory to a class of nonlinear systems. Based on the time domain interpretation of the NI property for LTI systems, a formal definition in terms of a dissipativity with an appropriate work rate will be used to define the nonlinear negative imaginary (NNI) property for a general nonlinear system. Mechanical systems with force actuators and position sensors are nonlinear negative imaginary according to this new definition. Using Lyapunov stability theory, we seek to establish a nonlinear generalization of the NI robust stability result for positive feedback interconnections of NNI systems. An example of a nonlinear mass-spring-damper system with force as input and displacement of the mass as output will be presented to illustrate the applicability of the NNI stability result. Furthermore, the case of NI systems with free motion will be investigated in the nonlinear domain based on the dissipativity framework of NNI systems.
