Abstract
This paper presents a stability theorem for a class of nonlinear fractional-order time-variant systems with fractional orderα (1<α<1)by using the Gronwall-Bellman lemma. Based on this theorem, a sufficient condition for designing a state feedback controller to stabilize such fractional-order systems is also obtained. Finally, a numerical example demonstrates the validity of this approach.
Highlights
Fraction-order system or system containing fractional derivatives and integrals has been studied widely [1,2,3,4,5]
This paper presents a stability theorem for a class of nonlinear fractional-order time-variant systems with fractional order α (0 ≤ α < 1) by using the Gronwall-Bellman lemma
It was found that many systems in interdisciplinary fields could be elegantly described with the help of fractional derivatives and integrals, such as viscoelastic system, dielectric polarization, electrode-electrolyte polarization, and electromagnetic waves [2,3,4]
Summary
Fraction-order system or system containing fractional derivatives and integrals has been studied widely [1,2,3,4,5]. Note that the existing LMI-based control methods for fractionalorder system only focus on the linear system but not on the case of nonlinear system To account this problem, based on the generalization of Gronwall-Bellman lemma, the analytical stability conditions and state feedback stabilization problem of nonlinear affine fractional-order system have been investigated in [16,17,18]. In [19], by using of MittagLeffler function, Laplace transform, and the generalized Gronwall inequality, a new sufficient condition ensuring local asymptotic stability and stabilization of a class of fractionalorder nonlinear systems with fractional-order α (1 < α < 2) was proposed. Motivated by the above mentioned works, the main purpose of this this paper is to consider the stability problem of a class of nonlinear fractional-order time-variant systems.
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