طراحی کنترل‌کننده مدلغزشی مبتنی بر پایداری رازومیخین و نامساوی ماتریسی خطی برای سیستم‌های غیر‌خطی مرتبه کسری تاخیری

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده علوم ریاضی، دانشگاه پیام نور، تهران، ایران

چکیده

ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ، ﺍﺯ ﻳﮏ ﮐﻨﺘﺮﻝ ﮐﻨﻨﺪﻩ ﻣﺪﻟﻐﺰﺷﻲ ﺑﺮﺍﻱ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﻏﻴﺮ ﺧﻄﻲ ﻭ ﻣﺮﺗﺒﻪ ﮐﺴﺮﻱ ﺗﺎﺧﻴﺮﻱ ، ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ

ﺍﺳﺖ. ﺳﻴﺴﺘﻢ ﺗﺤﺖ ﻣﻄﺎﻟﻌﻪ ﺩﺭ ﺣﻀﻮﺭ ﺍﻏﺘﺸﺎﺵ ﻭ ﻧﺎﻣﻌﻴﻨﻲ ﺍﺳﺖ. ﻫﺪﻑ ﻣﻘﺎﻟﻪ ﻃﺮﺍﺣﻲ ﮐﻨﺘﺮﻝ ﮐﻨﻨﺪﻩ ﻣﺪ ﻟﻐﺰﺷﻲ ﺑﻪﮔﻮﻧﻪﺍﻱ

ﺍﺳﺖ ﮐﻪ ﺳﻴﺴﺘﻢ ﻏﻴﺮ ﺧﻄﻲ ﭘﺎﻳﺪﺍﺭ ﻣﺠﺎﻧﺒﻲ ﺷﺪﻩ ﻭ ﻣﺘﻐﻴﺮﻫﺎﻱ ﺳﻴﺴﺘﻢ ﺩﺭ ﻳﮏ ﺯﻣﺎﻥ ﻣﺘﻨﺎﻫﻲ ﺑﻪ ﺳﻄﺢ ﻟﻐﺰﺵ ﺑﺮﺳﻨﺪ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ

ﺍﺯ ﻗﻀﻴﻪ ﺭﺍﺯﻭﻣﻴﺨﻴﻦ ﺑﺮﺍﻱ ﭘﺎﻳﺪﺍﺭﻱ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﮐﺴﺮﻱ ﺗﺎﺧﻴﺮﻱ ﻭ ﻧﺎﻣﺴﺎﻭﻱ ﻣﺎﺗﺮﻳﺴﻲ ﺧﻄﻲ، ﺷﺮﺍﻳﻂ ﻻﺯﻡ ﺑﺮﺍﻱ ﭘﺎﻳﺪﺍﺭﻱ ﺭﺍ

ﺑﻪ ﺩﺳﺖ ﻣﻲ ﺁﻭﺭﻳﻢ. ﺩﺭ ﻧﻬﺎﻳﺖ ، ﺑﺎ ﺩﻭ ﻣﺜﺎﻝ ﻋﺪﺩﻱ ﺻﺤﺖ ﻧﺘﺎﻳﺞ ﻭ ﮐﺎﺭﺍﻳﻲ ﺭﻭﺵ ﭘﻴﺶ ﻧﻬﺎﺩﻱ ﺭﺍ ﺑﺮﺭﺳﻲ ﮐﺮﺩﻩﺍﻳﻢ.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Design of sliding mode control based on Razumikhin approach and linear matrix inequality for nonlinear fractional time-varying delay systems

نویسندگان [English]

  • Mohammad Ghamgosar
  • Seyed Mehdi Mirhosseini-Alizamini
  • Mahmood Dadkhah
Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
چکیده [English]

In this paper, a sliding mode control for systems that are nonlinear, having fractional order, and

involve delay is used. The aim of this paper is to design a sliding mode controller, such that the closed­

looped nonlinear system becomes asymptotically stable and its trajectory can be driven onto the sliding

surface in finite time. By using the fractional Razumikhin theorem for the stability of fractional­ order

systems including delay and a linear matrix inequality, necessary conditions on asymptotic stabilization

are obtained. Some numerical examples are given to illustrate the effectiveness of the proposed results.

کلیدواژه‌ها [English]

  • Delay Systems
  • Fractional order systems
  • Sliding mode control
  • Linear Matrix Inequality
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