Robust stability analysis for a class of fractional order systems with uncertain parameters

Design an adaptive sliding mode controller for drive-response synchronization of two different uncertain fractional-order chaotic systems with fully unknown parameters

“…However, when the bounds are difficult to be found, the bounds are not supposed to be known constant. The bounds of the uncertainties and external disturbances are estimated by the adaptive laws (21) in this paper. This solves the problem that the bounds are unknown.…”

“…Generally speaking, chaos synchronization can be thought as the design problem of a feedback law for full observer using the known information of the plant, in order to ensure that the controlled receiver is synchronized with the transmitter. Now, synchronization of fractional-order systems has started to attract many attention [18][19][20][21][22][23][24][25]. Several methods have been proposed to achieve chaos synchronization.…”

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

“…Since fractional-order derivatives are nonlocal and have weakly singular kernels, the stability analysis of fractional-order differential equations is more complex than that of integer-order differential equations. In this sense, the stability of FOS has been extensively studied, for example, the continuous time FOS [3][4][5] and discrete time FOS [6]. In terms of linear matrix inequalities (LMIs), the stability condition has been given for a continuous FOS with fractional-order 0 < < 1 in [7] and 1 ≤ < 2 in [8].…”

Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation

“…Generally, some perturbations and uncertainties usually exist in these real world differential models due to some uncertain physical parameters and parametrical variations in time. These perturbations and uncertainties can be introduced in the underlying mathematical model [3,5,7,9,10,15,16,18].…”