Lyapunov‐Krasovskii stability analysis of delayed Filippov system: Applications to neural networks with switching control

Cai Zuowei; Huang Lihong

摘要

Summary >This paper gives the stability analysis of Filippov system with delay. Under the Filippov‐framework, we introduce a general type of Lyapunov‐Krasovskii functional (LKF) to derive the stability of delayed differential inclusions (DDIs), where the indefiniteness or positive definiteness of the derivative of LKF holds for almost everywhere along the trajectories of state solution. The proposed LKF of this paper generalizes the classic LKF whose derivative possesses negative definiteness or seminegative definiteness for everywhere. As a result, the stability, uniform stability, uniform asymptotic stability, and global exponential stability criteria of the trivial solution for DDI are established. Moreover, the developed LKF method is applied to solve the stabilization control issue of delayed neural networks, possessing discontinuous input‐output activation. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“main”XML：Lang =“en”XML：ID =“RNC4787-ABS-ABS-0001”> <标题类型=“main”>摘要</ title> <P>本文介绍了延迟Filippov系统的稳定性分析。在Filippov框架下，我们介绍了一般类型的Lyapunov-Krasovskii功能（LKF），以得出延迟差分夹杂物（DDIS）的稳定性，其中LKF的衍生物的衍生物的无限度或积极明确持有几乎沿着轨迹的各处国家解决方案。本文所提出的LKF概括了衍生物对各处都具有负面明确或神社会定义的经典LKF。结果，建立了稳定性，稳定性，均匀的渐近稳定性和DDI的普通解决方案的全局指数稳定性标准。此外，应用了开发的LKF方法来解决延迟神经网络的稳定控制问题，具有不连续的输入输出激活。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21736/'>《International Journal of Robust and Nonlinear Control》</a> <b style="margin: 0 2px;">|</b><span>2020年第2期</span><b style="margin: 0 2px;">|</b><span>共20页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Cai Zuowei&option=202" target="_blank" rel="nofollow">Cai Zuowei;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Huang Lihong&option=202" target="_blank" rel="nofollow">Huang Lihong;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Information TechnologyHunan Women's UniversityChangsha China;</p> <p>School of Mathematics and StatisticsChangsha University of Science and TechnologyChangsha China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/7742.html" title="自动化系统">自动化系统;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=control design&option=203" rel="nofollow">control design;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=neural networks&option=203" rel="nofollow">neural networks;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=nonlinear control&option=203" rel="nofollow">nonlinear control;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=nonlinear models and systems&option=203" rel="nofollow">nonlinear models and systems;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stability&option=203" rel="nofollow">stability;</a> </p> <div class="translation"> 机译：控制设计;神经网络;非线性控制;非线性模型和系统;稳定性; </div> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023067060.html">Lyapunov‐Krasovskii stability analysis of delayed Filippov system: Applications to neural networks with switching control</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Cai Zuowei&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Cai Zuowei,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Huang Lihong&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Huang Lihong </a> <a href="/journal-foreign-21736/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal of Robust and Nonlinear Control .</a> <span>2020</span><span>,第2期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：Lyapunov-Krasovskii延迟Filippov系统的稳定性分析：在具有开关控制的神经网络中的应用</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_journal-the-franklin-institute_thesis/0204119675001.html">Stability analysis of systems with time-varying delays using overlapped switching Lyapunov Krasovskii functional</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abolpour Roozbeh&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Abolpour Roozbeh,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Dehghani Maryam&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Dehghani Maryam,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Talebi Heidar Ali&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Talebi Heidar Ali </a> <a href="/journal-foreign-635/" target="_blank" rel="nofollow" class="tuijian_authcolor">Journal of the Franklin Institute .</a> <span>2020</span><span>,第15期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用重叠切换Lyapunov Krasovskii功能的时变延迟的系统稳定性分析</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/academic-journal-foreign_communications-nonlinear-science-and-numerical-simulation_thesis/0204111728957.html">On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov-Krasovskii functional</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=O.M. 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href="/patent-detail/06120101771393.html">具有延迟补偿能力的触控面板系统以及用于触控面板系统中补偿延迟的方法</a> <b>[P]</b> . <span> 中国专利： CN102999205A </span> <span> . 2013-03-27</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130449098176.html">Process for controlling the transmission of traffic sensitive to delay and not sensitive to the retardation of a plurality of network nodes to a central node on a shared medium.In packet switched communication network includes a central node and a plurality of network nodes connected to the mentioned central node for a half share, and.The node in a packet switched communication network in to control the data transmission of a plurality of network nodes over a shared medium</a> <b>[P]</b> . <span> 外国专利：  BR9915806A </span> <span> . 2001-08-21</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：控制对延迟敏感而不对多个网络节点的延迟敏感的业务向共享介质上的中心节点的传输的过程。在分组交换通信网络中，包括中心节点和连接到所述节点的多个网络节点分组交换通信网络中的该节点控制共享共享介质上多个网络节点的数据传输 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130438907808.html">Internal combustion engine controlling device, has delay units disposed in upstream of neural network for taking into account history of operation of internal combustion engine, and delay selection unit disposed in upstream of network</a> <b>[P]</b> . <span> 外国专利：  FR2867519A1 </span> <span> . 2005-09-16</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：内燃发动机控制装置，具有设置在神经网络上游以考虑内燃机的运行历史的延迟单元，以及配置在网络上游的延迟选择单元 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130403284505.html">Neural network system for single processing common operation group of neural network models application processor including same and operation method of neural network system</a> <b>[P]</b> . <span> 外国专利：  KR20190055610A </span> <span> . 2019-05-23</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于神经网络的单处理通用操作组的神经网络系统模型应用处理器及其包括的神经网络系统的操作方法 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704023067060','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" style="display: none"> <div class="journal-sub"> 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