A new robust fractional order sliding mode control considering interval mismatch for fractional order uncertain time-varying delay systems

Abstract This paper concentrates on the robust fractional sliding mode control for fractional uncertain time-varying delay systems in order (0,1). By providing a novel Lyapunov–Krasovskii function, some novel conditions considering interval mismatch are derived to obtain a linear quadratic regulator (LQR) based fractional sliding mode control (SMC) strategy. Based on a fractional order integral matrix inequality and linear matrix inequality (LMI) approach, the conditions are less conservative and easy to solve. The control law is designed by using hyperbolic tangent function to reduce chattering phenomenon. The proposed conditions can be solved using some standard numerical packages. Two examples are provided to verify the effectiveness of the introduced theoretical formulation.