Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances

The problem of designing a sliding-mode controller for a class of fractional-order uncertain linear perturbed systems with Caputo derivative is addressed in this paper. Sufficient conditions for the existence of sliding surfaces guaranteeing the asymptotic stability of the reduced-order sliding-mode dynamics are obtained in terms of linear matrix inequalities, based on which and stability theory of fractional-order nonlinear systems; the corresponding reaching motion controller is proposed, and the reaching time is also obtained. Moreover, the upper bounds of the nonlinear uncertainties are not required to be known in advance, which can be tuned by the designed adaptive law. Meanwhile, some problems for the sliding-mode controller for fractional-order systems in existing literatures are pointed out. A numerical example is presented to demonstrate the validity and feasibility of the obtained results.