Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties
This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical s...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2022-05-01
|
| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/27486 |
| _version_ | 1818533912984420352 |
|---|---|
| author | L. Susana Ramya Rathinasamy Sakthivel Chao Wang |
| author_facet | L. Susana Ramya Rathinasamy Sakthivel Chao Wang |
| author_sort | L. Susana Ramya |
| collection | DOAJ |
| description |
This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system.
|
| first_indexed | 2024-12-11T18:04:58Z |
| format | Article |
| id | doaj.art-a556564478f04e96959ec240e5072657 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-11T18:04:58Z |
| publishDate | 2022-05-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-a556564478f04e96959ec240e50726572022-12-22T00:55:46ZengVilnius University PressNonlinear Analysis1392-51132335-89632022-05-012710.15388/namc.2022.27.27486Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertaintiesL. Susana Ramya0Rathinasamy Sakthivel1Chao Wang2Dr. NGP Institute of TechnologyBharathiar UniversityYunnan University This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system. https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/27486fractional-order differential systemreliable nonfragile controllerfinite-time controlasymmetric input saturationstructured uncertainty |
| spellingShingle | L. Susana Ramya Rathinasamy Sakthivel Chao Wang Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties Nonlinear Analysis fractional-order differential system reliable nonfragile controller finite-time control asymmetric input saturation structured uncertainty |
| title | Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| title_full | Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| title_fullStr | Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| title_full_unstemmed | Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| title_short | Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| title_sort | finite time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties |
| topic | fractional-order differential system reliable nonfragile controller finite-time control asymmetric input saturation structured uncertainty |
| url | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/27486 |
| work_keys_str_mv | AT lsusanaramya finitetimereliablenonfragilecontrolforfractionalordernonlinearsystemswithasymmetricalsaturationandstructureduncertainties AT rathinasamysakthivel finitetimereliablenonfragilecontrolforfractionalordernonlinearsystemswithasymmetricalsaturationandstructureduncertainties AT chaowang finitetimereliablenonfragilecontrolforfractionalordernonlinearsystemswithasymmetricalsaturationandstructureduncertainties |