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

ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ، ﺍﺯ ﻳﮏ ﮐﻨﺘﺮﻝ ﮐﻨﻨﺪﻩ ﻣﺪﻟﻐﺰﺷﻲ ﺑﺮﺍﻱ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﻏﻴﺮ ﺧﻄﻲ ﻭ ﻣﺮﺗﺒﻪ ﮐﺴﺮﻱ ﺗﺎﺧﻴﺮﻱ ، ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩﺍﺳﺖ. ﺳﻴﺴﺘﻢ ﺗﺤﺖ ﻣﻄﺎﻟﻌﻪ ﺩﺭ ﺣﻀﻮﺭ ﺍﻏﺘﺸﺎﺵ ﻭ ﻧﺎﻣﻌﻴﻨﻲ ﺍﺳﺖ. ﻫﺪﻑ ﻣﻘﺎﻟﻪ ﻃﺮﺍﺣﻲ ﮐﻨﺘﺮﻝ ﮐﻨﻨﺪﻩ ﻣﺪ ﻟﻐﺰﺷﻲ ﺑﻪﮔﻮﻧﻪﺍﻱﺍﺳﺖ ﮐﻪ ﺳﻴﺴﺘﻢ ﻏﻴﺮ ﺧﻄﻲ ﭘﺎﻳﺪﺍﺭ ﻣﺠﺎﻧﺒﻲ ﺷﺪﻩ ﻭ ﻣﺘﻐﻴﺮﻫﺎﻱ ﺳﻴﺴﺘﻢ ﺩﺭ ﻳﮏ ﺯﻣﺎﻥ ﻣﺘﻨﺎﻫﻲ ﺑﻪ ﺳﻄﺢ ﻟﻐﺰﺵ ﺑﺮﺳﻨﺪ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩﺍﺯ ﻗﻀﻴﻪ ﺭﺍﺯﻭﻣﻴﺨﻴﻦ ﺑﺮﺍﻱ ﭘﺎﻳﺪﺍﺭﻱ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﮐﺴﺮﻱ ﺗﺎﺧﻴﺮﻱ ﻭ ﻧﺎﻣﺴﺎﻭﻱ ﻣﺎﺗﺮﻳﺴﻲ ﺧﻄﻲ، ﺷﺮﺍﻳﻂ ﻻﺯﻡ ﺑﺮﺍﻱ ﭘﺎﻳﺪﺍﺭﻱ ﺭﺍﺑﻪ ﺩﺳﺖ ﻣﻲ ﺁﻭﺭﻳﻢ. ﺩﺭ ﻧﻬﺎﻳﺖ ، ﺑﺎ ﺩﻭ ﻣﺜﺎﻝ ﻋﺪﺩﻱ ﺻﺤﺖ ﻧﺘﺎﻳﺞ ﻭ ﮐﺎﺭﺍﻳﻲ ﺭﻭﺵ ﭘﻴﺶ ﻧﻬﺎﺩﻱ ﺭﺍ ﺑﺮﺭﺳﻲ ﮐﺮﺩﻩﺍﻳﻢ.

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

In this paper, a sliding mode control for systems that are nonlinear, having fractional order, andinvolve delay is used. The aim of this paper is to design a sliding mode controller, such that the closed­looped nonlinear system becomes asymptotically stable and its trajectory can be driven onto the slidingsurface in finite time. By using the fractional Razumikhin theorem for the stability of fractional­ ordersystems including delay and a linear matrix inequality, necessary conditions on asymptotic stabilizationare obtained. Some numerical examples are given to illustrate the effectiveness of the proposed results.