不确定性负虚系统的绝对稳定性研究  

Absolute Stability of Negative Imaginary System with Uncertainty

作　　者：陈阵 CHEN Zhen(School of Information Science and Technology,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学信息科学技术学院,安徽合肥230026

出　　处：《测控技术》2021年第2期123-129,144,共8页Measurement & Control Technology

基　　金：国家自然科学基金面上项目(61773357)。

摘　　要：负虚性质广泛存在于各种工程应用中,受到了广大控制领域学者的关注,但是目前对于负虚系统理论的研究局限于负虚系统定义、性质的延伸和线性系统理论部分,忽略了实际场景中存在的不确定性。为此,针对斜率有界、无记忆的不确定性和负虚被控对象以及严格负虚控制器的互连系统,利用环变换、卡尔曼分解等方法将系统变为线性部分和非线性部分的并联,进而利用Lur'e-Postnikov型李亚普诺夫函数提出了互连系统的绝对稳定性条件。并且,在负虚系统和不确定性部分已知时,给出了使整个系统绝对稳定的严格负虚控制器的DC增益条件,并通过两个数值仿真实例验证了所提理论的正确性和有效性。Negative imaginary property is a property exhibited in many engineering applications,which has attracted more and more attention of researchers in control theory filed.So far,the research mainly focused on the extension of the definition and properties of negative imaginary system and the theory of linear system,while ignoring the uncertain part.Therefore,for the interconnected system with slope-restricted,memoryless uncertainty,negative imaginary controlled object and strictly negative imaginary controller,the loop transformation and Kalman decompositionto are used to convert the system into linear and nonlinear parts,and then the Lur^e-Postnikov type Lyapunov function is used to give the absolute stability conditions of the system.When the negative imaginary system and the uncertainty part are known,the DC gain conditions of the strict negative imaginary controller which makes the whole system absolutely stable is given.Finally,two numerical simulation examples verify the correctness and effectiveness of the developed theory.

关 键 词：负虚系统 绝对稳定性 环变换 不确定性 严格负虚系统 

分 类 号：TP202[自动化与计算机技术—检测技术与自动化装置]