Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

Tavazoei Mohammad; Asemani Mohammad Hassan

摘要

Summary > This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for type="mathematics"> <fi>L</fi> <sub>2</sub> ‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in type="mathematics">(0.5,?1) or type="mathematics">(1.5,?2) . Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H <sub>∞</sub> ‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results. </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 XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”> <title type =“main”>摘要</ title> >本文专注于提出稳定性分析的新条件和非线性分数级系统类别的稳定化。首先，通过将非线性分数阶系统的类作为反馈互连系统和应用小增益定理，提出了<跨度类型=“数学”> <fi> l </ fi> <sub> 2 < / sub> </ span> - 这些系统的解决方案的界限。然后，通过使用Mittag-Leffler函数属性，我们表明，提出的条件的满足证明了在<跨度类型=“数学”>（0.5 ,? 1）</ span>或 type =“数学”>（1.5，？2）</ span>。与基于Lyapunov的稳定性分析方法不同，新条件取决于系统的分数顺序。此外，它与系统的线性部分的H <sub>∞</ sub> norm有关，并且可以使用分数级界限真实的引理来转化为线性矩阵不等式（LMI）。此外，所提出的稳定性分析方法延伸到基于求解一些LMI的非线性分数级系统类别的状态反馈和基于观察者的控制器设计。在基于观察者的稳定问题中，我们证明了分离原理使用我们的方法持有，并且可以在两个单独的步骤中找到观察者增益和假级反馈增益。最后，提供了三个数值例子以证明具有先前结果的新颖提出条件的优点。 </ p> </ abstract> </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>2018年第15期</span><b style="margin: 0 2px;">|</b><span>共16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=Tavazoei Mohammad&option=202" target="_blank" rel="nofollow">Tavazoei Mohammad;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Asemani Mohammad Hassan&option=202" target="_blank" rel="nofollow">Asemani Mohammad Hassan;</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>School of Electrical and Computer EngineeringShiraz UniversityShiraz Iran;</p> <p>School of Electrical and Computer EngineeringShiraz UniversityShiraz Iran;</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=H ∞ ‐norm&option=203" rel="nofollow">H ∞ ‐norm;</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 fractional‐order system&option=203" rel="nofollow">nonlinear fractional‐order system;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=observer‐based stabilization&option=203" rel="nofollow">observer‐based stabilization;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=pseudostate feedback&option=203" rel="nofollow">pseudostate feedback;</a> </p> <div class="translation"> 机译：H∞-norm;非线性控制;非线性分数阶系统;基于观察者的稳定;假稳定反馈; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 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