Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties
Articles
L. Susana Ramya
Dr. NGP Institute of Technology
Rathinasamy Sakthivel
Bharathiar University
https://orcid.org/0000-0002-5528-2709
Chao Wang
Yunnan University
Published 2022-05-09
https://doi.org/10.15388/namc.2022.27.27486
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Keywords

fractional-order differential system
reliable nonfragile controller
finite-time control
asymmetric input saturation
structured uncertainty

How to Cite

Ramya, L.S., Sakthivel, R. and Wang, C. (2022) “Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties”, Nonlinear Analysis: Modelling and Control, 27(4), pp. 766–788. doi:10.15388/namc.2022.27.27486.

Abstract

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.

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