Adaptive fault‐tolerant control for fractional‐order fuzzy financial time‐delay system

Abstract

This work is allocated to investigate the problem of stabilization and fault tracking of fractional‐order (FO) fuzzy financial time‐delay system. And some situations that affect or collapse the whole system are taken into account as faults in system states. Precisely, an observer‐based controller that incorporates the estimated‐fault is introduced into the addressed system to handle these kinds of faults, and is called fuzzy fault‐tolerant controller. Moreover, a novel class of linear‐matrix‐inequality (LMI) constrains are derived forasymptotic stability of addressed system by using Lyapunov–Krasovskii (LK) functional employee. At last, a numerical example part includes two samples are given to assist the derived theoretical results.

Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model

“…911-933 ISSN 2775-2658 Proof. Suppose the solution of (7) be denoted as W(t) and let the solution for (15) be W * (t). For ϵ > 0, and using the Laplace transform method, the subsequent steps are obtained,…”

Stabilization of nonlinear fractional order faulty systems with time-varying delay

“…On the other hand, time-delay takes place in the majority of practical systems and influences the performance of systems and may bring about instability Phat et al, 2020). The problem of FTC for nonlinear fractional order systems in the presence of time-delay has been noticed in several research studies (Sundarrajan and Palanisami, 2021;Sweetha et al, 2022). An adaptive FTC has been established for fractional order fuzzy financial time-delay system in Sundarrajan and Palanisami (2021).…”

“…The problem of FTC for nonlinear fractional order systems in the presence of time-delay has been noticed in several research studies (Sundarrajan and Palanisami, 2021;Sweetha et al, 2022). An adaptive FTC has been established for fractional order fuzzy financial time-delay system in Sundarrajan and Palanisami (2021). The issue of non-fragile FTC for nonlinear fractional order systems with distributed delays has been studied in Sweetha et al (2022).…”

“…Delay-independent stability criteria are beneficial when time-delay is unknown. Stability proof of fractional order time-delay systems based on delaydependent Lyapunov-Krasovskii functional (LKF) just has been considered in a few researches (Sundarrajan and Palanisami, 2021;Sweetha et al, 2022). In and Cheng et al (2021), some new delay-dependent LKFs have been introduced for studying the stability of fractional order time-delay systems, but in these literatures, fault has not been taken into account in the system equations.…”