非线性系统的负虚系统理论：耗散性方法
Negative Imaginary Systems Theory for Nonlinear Systems: A Dissipativity Approach
摘要：
负虚系统（NI）理论是分析和设计线性时不变（LTI）控制系统的一个成熟的系统理论框架。本文将负虚系统理论推广到一类非线性系统。基于对线性时不变系统负虚部特性的时域解释，利用耗散性和适当的功率给出了一般非线性系统的非线性负虚部（NNI）特性的形式定义.根据这个新定义，具有力致动器和位置传感器的机械系统是非线性负虚的。利用李雅普诺夫稳定性理论，我们试图建立一个非线性推广的NI鲁棒稳定性结果的正反馈互联的NNI系统。一个非线性质量-弹簧-阻尼器系统的力作为输入和质量的位移作为输出的例子将被提出来说明NNI稳定性结果的适用性。此外，NI系统的情况下，自由运动将研究在非线性域的基础上耗散框架的NNI系统。
英文摘要：
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.
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