A sliding mode control for linear fractional systems with input and state delays

By Amar Si-Ammour, S. Djennoune, Maamar Bettayeb. 2009

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Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics (2010, methodology): “Sliding manifolds containing fractional-order derivatives were used in both works [23, 24].”
Integral sliding mode control for fractional-order systems with mismatched uncertainties (2013, background): “In addition, the fractionalorder sliding mode controllers for fractional-order systems with input-delays and nonlinear terms have been studied in [15–18].”
On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics (2016, methodology): “Although fractional calculus has been previously combined with the sliding-mode control methodology in the controller design for conventional integer-order systems [14, 15], sliding-mode control has been applied to fractional-order systems only recently [14, 16, 17].”
Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ (2013, background): “The main feature of SMC [23–25,30–32] is to switch the control law to force the states of the system from the initial states onto some predefined sliding surface.”
Fractional order sliding mode control with reaching law approach (2010, methodology): “Solution of the state equation is built and conclusions involving Mittag-Leffler function are derived for stability, [16].”