基于观测器的时变时滞单边Lipschitz系统镇定  

Stabilizing the one-sided Lipschitz system with time-varying delay based on an observer

作　　者：黄玲[1] 钟贝贝 HUANG Ling;ZHONG Bei-bei(School of Automation,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学自动化学院,哈尔滨150080

出　　处：《电机与控制学报》2020年第10期144-152,共9页Electric Machines and Control

基　　金：国家自然科学青年基金(61304046);黑龙江省科学基金项目(LH2020F035)。

摘　　要：针对现有单边Lipschitz系统进行镇定时不考虑时滞信息,无法充分利用系统信息进行系统综合的情况,讨论基于观测器的一种新的镇定控制器设计问题。首先,对于带有时变时滞的单边Lipschitz非线性系统的状态构造观测器,基于构造状态设计由原状态和时滞状态共同决定的控制器,然后依据Lyapunov稳定性理论,采用改进的Wirtinger不等式、Young’s不等式、Schur补引理、单边Lipschitz条件以及二次内有界条件,将出现的非线性项转化为可处理的线性项,推导出使基于状态观测器的控制器存在的充分条件。该条件不仅与系统原状态及时滞状态相关,而且与观测器的原状态以及时滞状态有关。对不等式进行求解,从而得出控制器以及观测器的增益矩阵。最后,利用2个数值例子验证提出方法的有效性。Aiming at the problem that the existing one-sided Lipschitz system does not consider the delay information and cannot make full use of the system information,the design of a stabilization controller based on an observer is discussed.First,for the state construction observer of one-sided Lipschitz nonlinear system with time-varying delay,the controller determined by the original state and the delay state was designed based on the construction state.Then,according to Lyapunov stability theory,the improved Wirtinger inequality,Young’s inequality,Schur complement lemma,one-sided Lipschitz condition and quadratic bounded condition were used to transform the nonlinear terms into the linear terms that can be dealt with,and the sufficient conditions for the existence of the controller based on the state observer were derived.The condition was related to the original state of the system,and the original state of the observer and the time delay state.The gain matrices of the controller and the observer were obtained by solving the inequality.Finally,two numerical examples were used for testing the feasibility of the proposed method.

关 键 词：单边Lipschitz系统 时变时滞 WIRTINGER不等式 

分 类 号：TP271.6[自动化与计算机技术—检测技术与自动化装置]