{"id":92244,"date":"2016-07-09T04:32:43","date_gmt":"2016-07-09T04:32:43","guid":{"rendered":"http:\/\/healthmedicinet.com\/i\/global-ot-%ce%b1-stabilization-of-fractional-order-memristive-neural-networks-with-time-delays\/"},"modified":"2016-07-09T04:32:43","modified_gmt":"2016-07-09T04:32:43","slug":"global-ot-%ce%b1-stabilization-of-fractional-order-memristive-neural-networks-with-time-delays","status":"publish","type":"post","link":"https:\/\/healthmedicinet.com\/i\/global-ot-%ce%b1-stabilization-of-fractional-order-memristive-neural-networks-with-time-delays\/","title":{"rendered":"Global \n\n\nO\n(\n\nt\n\n–\n?\n\n\n)\n\n\n stabilization of fractional-order memristive neural networks with time delays"},"content":{"rendered":"

Recently, the fractional calculus serving the fractional-order models develops fast in both theoretical and application. The analysis about fractional-order models has attracted increasing attention cause of its promising applications in various areas of science and engineering (see Chen and Chen 2015<\/a><\/span>; Chen et\u00a0al. 2014<\/a><\/span>; Liu et\u00a0al. 2015<\/a><\/span>; Liang et\u00a0al. 2015<\/a><\/span>; Li et\u00a0al. 2015<\/a><\/span>; Rakkiyappan et\u00a0al. 2014<\/a><\/span>, 2015b<\/a><\/span>; Stamova 2014<\/a><\/span>; Velmurugan and Rakkiyappan 2016<\/a><\/span>; Velmurugan et\u00a0al. 2016<\/a><\/span>; Wang et\u00a0al. 2014<\/a><\/span>; Wu and Zeng 2016<\/a><\/span>; Wu et\u00a0al. 2016<\/a><\/span>). Comparing with integer-order systems, fractional-order systems show the superiority of describing and modeling the real world or the practical problems such as anomalous diffusion, signal processing, fractal theory and continuum mechanics. Whereas, it is arduously to promote the development of research about fractional-order models for the absence of efficient mathematical tools. As mentioned by Chen and Chen (2016<\/a><\/span>), Chen et\u00a0al. (2014<\/a><\/span>), some new and useful methods for the qualitative analysis of fractional-order models are very imperative.<\/p>\n

On the other hand, memristor is a circuit element which was proposed by Chua (1971<\/a><\/span>) and has been realized the prototype by Hewlett-Packard laboratory in Strukov et\u00a0al. (2008<\/a><\/span>) and Tour and He (2008<\/a><\/span>). Different from classical resistors, memristor is a nonlinear resistor which owns non-uniqueness values. In addition, the memristor can manage and store a great quantity of information. For its excellent properties about memory, we can build a new model if the conventional resistors are replaced by the memristors in neural networks, which is called memristive neural networks. Some representative works studied on the properties of the memristive systems display its applicability in several interdisciplinary areas (see Bao and Zeng 2013<\/a><\/span>; Guo et\u00a0al. 2015<\/a><\/span>; Wang et\u00a0al. 2003<\/a><\/span>; Wu et\u00a0al. 2012<\/a><\/span>; Wu and Zeng 2012<\/a><\/span>; Wen and Zeng 2012<\/a><\/span>; Zhao et\u00a0al. 2015<\/a><\/span>). From the description of memristive neural networks, combining memristors with infinite memory is extremely interesting. An advantage of fractional-order systems in comparison to integer-order systems is that fractional-order systems can generate infinite memory. Therefore, merging the memristors into a class of fractional-order neural networks is pretty anticipated. Although stability analysis of fractional-order memristive or memristor-based neural networks has been gradually carried out (see Chen et\u00a0al. 2014<\/a><\/span>, 2015<\/a><\/span>; Rakkiyappan et\u00a0al. 2014<\/a><\/span>, 2015b<\/a><\/span>; Velmurugan and Rakkiyappan 2016<\/a><\/span>; Velmurugan et\u00a0al. 2016<\/a><\/span>), it is worth noting that fractional-order memristive neural networks can exhibit complicated dynamics or chaotic behaviors if the network\u2019s parameters and time delays are appropriately specified.<\/p>\n

Noticed that many static or dynamic control laws have been designed to stabilize nonlinear control systems, for instance, Chandrasekar and Rakkiyappan (2016<\/a><\/span>), Chen et\u00a0al. (2015<\/a><\/span>), Guo et\u00a0al. (2013<\/a><\/span>), Huang et\u00a0al. (2009<\/a><\/span>), Lou et\u00a0al. (2013<\/a><\/span>), Mathiyalagan et\u00a0al. (2015<\/a><\/span>), Rakkiyappan et\u00a0al. (2015a<\/a><\/span>), Wu et\u00a0al. (2016<\/a><\/span>), Yang and Tong (2016<\/a><\/span>). In allusion to different system structures and actual control requirements, lots of stabilization criteria are established, for example, periodic intermittent stabilization (Huang et\u00a0al. 2009<\/a><\/span>), robust stabilization (Yang and Tong 2016<\/a><\/span>), finite-time stabilization (Zhang et\u00a0al. 2016<\/a><\/span>), impulsive stabilization (Chandrasekar and Rakkiyappan 2016<\/a><\/span>; Huang 2010<\/a><\/span>; Lou et\u00a0al. 2013<\/a><\/span>). Despite these fruitful achievements, some stabilization approaches can hardly be widely applied in practical problems due to high gain. In addition, an undeniable fact is that stabilization control schemes of fractional-order systems is little studied. Hence, it is necessary to investigate some appropriate controllers for stabilization of fractional-order systems.<\/p>\n

Inspired by the above discussion, in this article, we will study the global (O(t^{-alpha }))<\/span> stabilization problem for a class of fractional-order memristive neural networks with time delays. We first introduce the concepts about fractional calculation and global stabilization of fractional-order systems. Secondly, for exploring some simple useful controllers, linear state feedback control law and linear output feedback control law are designed to stabilize the fractional-order systems. In addition, stabilization criteria in form of algebraic inequalities are derived by utilizing a new fractional Lyapunov method instead of classical Gronwall inequality. The conditions can be easily verified.<\/p>\n","protected":false},"excerpt":{"rendered":"

Recently, the fractional calculus serving the fractional-order models develops fast in both theoretical and application. The analysis about fractional-order models has attracted increasing attention cause of its promising applications in various areas of science and engineering (see Chen and Chen 2015; Chen et\u00a0al. 2014; Liu et\u00a0al. 2015; Liang et\u00a0al. 2015; Li et\u00a0al. 2015; Rakkiyappan et\u00a0al. Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-92244","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/posts\/92244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/comments?post=92244"}],"version-history":[{"count":0,"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/posts\/92244\/revisions"}],"wp:attachment":[{"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/media?parent=92244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/categories?post=92244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/healthmedicinet.com\/i\/wp-json\/wp\/v2\/tags?post=92244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}