Second-order sliding mode control for nonlinear fractional-order systems

Novel results on nonlinear fractional-order systems (FOSs) with second-order sliding mode control (SMC) is presented. The controller is designed by proposing a fractional switching surface and it is useful to achieve the finite-time reachability condition. The main objective is to adapt the linear quadratic regulator (LQR) performance in the analysis to improve the transient performance of the FOSs. Further, some unique conditions are derived by using Lyapunov theory and linear matrix inequalities (LMIs). Finally, the results are verified with a Chua's circuit model to illustrate the usefulness.