Robust Mittag‐Leffler stabilisation of fractional‐order systems

Abstract

Dynamic models approximate physical phenomena to certain extent and ideal controllers are proposed. Nevertheless, when system specifications crave for better performance, additional robust controllers are considered. In this sense, a robust controller is proposed in this paper, which accounts for a general class of fractional-order systems, in order to compensate for matched and mismatched disturbances. The Mittag-Leffler stability of the solution of the closed-loop system is demonstrated for a class of fractional-order systems subject to non-smooth effects and control feedback. Numerical simulations are conducted to highlight the reliability of the proposed scheme.

Passive Fault-Tolerant Control of a 2-DOF Robotic Helicopter

“…The nonlinear controller u NL aims to compensate gravitational torques. LMI based robust controllers with a nonlinear compensation of uncertainties have been proposed in [23], for the case of fractional-order systems, and without considering the presence of faults. By substituting the controller (4) into (3), one obtains…”

Description and analysis of the time–domain response of nabla discrete fractional order systems

“…< n, n ∈ Z + , then the time-domain response to the fractional order system (19) with u(k) ≡ 0 has the following properties:…”

“…Fractional calculus is a natural generalization of classical calculus and its inception can be traced back to the year 1695, when Leibniz provided the possible value of a half order derivative (see page 1 and page 3 of [20], page xi and page 1 of [17], page xxvii of [27] and page xvii of [25]). After over 300 years of development, fractional calculus has been widely used in many branches of science and engineering, and is particularly suitable for modeling and control physical plants [14,26] (see some other excellent papers [19,28,37] and their references for many examples).…”

Lyapunov functions for fractional‐order nonlinear systems with Atangana–Baleanu derivative of Riemann–Liouville type

“…In recent papers, some families of operators that involve generalized kernels in the fractional integral were proposed 35–38 . These operators can generalize classical results, for example, the stability analysis of the dynamic systems associated with these derivatives through Lyapunov methods or the study of the Ulam–Hyers–Rassias stability problem 39–45 …”

“…[35][36][37][38] These operators can generalize classical results, for example, the stability analysis of the dynamic systems associated with these derivatives through Lyapunov methods or the study of the Ulam-Hyers-Rassias stability problem. [39][40][41][42][43][44][45] Recently, 46 a significant progress was made in the stability theory of fractional-order systems with Atangana-Baleanu derivative of Caputo type, such that, the Lyapunov direct method can be considered throughout some interesting novel inequalities.…”