Sliding mode control for fractional-order time-varying delay systems under external excitation

In this paper, by using Lyapunov–Krasovskii stability theory and linear matrix inequality approach, the control problem for fractional-order systems under seismic waves with time-varying delays is studied. A novel switching surface is proposed. Based on the linear quadratic regulator and sliding mode control, some sufficient conditions are derived to ensure the fractional system under control. Mittag-Leffler stability theorem is adopted to prove that the switching surface could converge to zero. Finally, a numerical simulation example is provided to validate the advantages and effectiveness of the proposed results.