基于积分不等式的时滞系统稳定性研究

发布时间：2019-06-26 21:16

【摘要】：时滞现象大量存在于网络控制系统、机械传动系统以及经济系统等各类系统中。时滞往往导致动态性能不良,甚至不稳定,同时在某些控制系统中时滞又可以改善控制效果。因此对时滞系统的稳定性研究在系统与控制领域中有重要的理论意义和现实价值,近年来得到了国内外学者的广泛关注。首先,本文总结了目前研究时滞稳定性的主要方法,重点对积分不等式方法进行了深入的研究,进而针对连续时滞系统提出了一种新的研究时滞相关稳定性的积分不等式方法——推广的二重积分不等式方法。针对离散时滞系统,提出了新的基于Abel型有限和不等式的离散不等式方法。这两个不等式将包含更多时滞信息项。特别地,许多文献比较了积分不等式的方法和自由权矩阵的方法,尽管两种方法在对导数项的估计和放大程度的效果上几乎相当,但积分不等式的方法表达形式简洁,减少很多决策变量,减轻了计算负担,因而积分不等式方法展现出了其优越性。其次,应用新的不等式,并结合Lyapunov泛函方法,分别针对分布时滞系统,中立型时滞系统,广义时滞系统和离散时滞系统这四种情况,研究了时滞系统的时滞相关稳定性,得到了基于线性矩阵不等式(LMIs)的一系列时滞相关稳定性判据,所得结果从理论和数值例子上加以说明该方法具有较小的保守性。最后,对全文所做的工作进行了总结,并指出了下一步研究的方向。
[Abstract]:The phenomenon of time delay exists in many kinds of systems, such as network control system, mechanical transmission system, economic system and so on. Time delay often leads to poor dynamic performance and even instability. At the same time, time delay can improve the control effect in some control systems. Therefore, the study of the stability of time-delay systems has important theoretical significance and practical value in the field of system and control, and has been widely concerned by scholars at home and abroad in recent years. Firstly, this paper summarizes the main methods to study the stability of time delay, with emphasis on the integral inequality method, and then proposes a new integral inequality method for continuous time delay systems, which is the extended double integral inequality method, which studies the delay dependent stability. A new discrete inequality method based on Abel type finite sum inequality is proposed for discrete time-delay systems. These two inequalities will contain more information terms with time delay. In particular, many literatures compare the method of integral inequality with the method of free matrix. Although the two methods have almost the same effect on the estimation and amplification of derivative terms, the method of integral inequality is simple in expression, reduces many decision variables and lightens the burden of calculation, so the method of integral inequality shows its advantages. Secondly, by using the new inequality and Lyapunov functional method, the delay-dependent stability of time-delay systems is studied for distributed time-delay systems, neutral time-delay systems, generalized time-delay systems and discrete time-delay systems, respectively. A series of delay-dependent stability criteria based on linear matrix inequality (LMIs) are obtained. The results show that the method is less conservative in theory and numerical examples. Finally, the work done in this paper is summarized, and the direction of the next research is pointed out.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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