Stabilization using fractional-order PI and PID controllers

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Stability of Fractional-Order Systems with Rational Orders (2008, unknown): “Moreover, modern control method as for example LMI (Linear Matrix Inequality) methods [43] or other algorithms [29, 30] already have been developed.”
Fractional order sliding mode control with reaching law approach (2010, methodology): “Stabilization of a fractional order system with a fractional order PID is presented in [6], the parameter selection issues utilizing the rules inspired from the Ziegler-Nichols approach is presented in [7].”
Observer-Based Sliding Mode Control for a Class of Noncommensurate Fractional-Order Systems (2015, methodology): “, have been replaced using fractional variants enhancing the scope of control theory [12], [13].”
Integral sliding mode control for fractional-order systems with mismatched uncertainties (2013, methodology): “Because PID control is applied widely in the industry fields, many design methods for fractional-order PID control are studied [6, 7].”
Rational approximation for fractional-order system by particle swarm optimization (2012, background): “cn in engineering [1], for example, in heat diffusion modeling and control [2–4], the fractional-order PID controller [5–7], fractional-order chaotic systems [8–10], the fractional-order digital filter [11, 12], etc.”