Abstract
This paper considers a class of semilinear fractional-order systems with Caputo derivative. New conditions ensuring asymptotic stability and stabilization of fractional systems with the fractional order between 0 and 2 are proposed. The analysis is based on a property of convolution and asymptotic properties of Mittag-Leffler functions. Some numerical examples are provided to illustrate the feasibility and validity of the proposed approach.
Highlights
Over the past several decades, fractional calculus has attracted much attention from scientists and engineers. is is because fractional differential equations have proven to be effective in modelling many physical phenomena and have been applied in different science and engineering fields
Significant contributions have been proposed in fractional differential equations both in theory and applications
In 1996, Matignon studied the stability of linear fractional differential equations in [5], which is regarded as the first work in this area
Summary
Over the past several decades, fractional calculus has attracted much attention from scientists and engineers. is is because fractional differential equations have proven to be effective in modelling many physical phenomena and have been applied in different science and engineering fields. Li et al investigated the Mittag-Leffler stability of nonlinear fractional dynamic systems in [6] and suggested the Lyapunov direct method for nonlinear fractional-order stability systems [7]. Ere has been more literature on stability of dynamic fractional-order systems, in which important and sufficient conditions were discussed for the stability of linear and linear time-delay fractional differential equations as stated in [8–10]. Erefore, based on this theory of stability, a basic criterion for stabilizing a class of nonlinear fractional-order systems is derived, in which control parameters can be selected through the linear control theory pole placement technique. The results obtained can be used to stabilize the class of fractional-order nonlinear systems by means of a linear state feedback controller.
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