Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions

This paper considers the second-order sliding (2-sliding) mode control design problem for nonlinear systems with uncertainties bounded by positive functions. Two different 2-sliding mode control algorithms are proposed, including a discontinuous one and a quasi-continuous one. The discontinuous algorithm is built based upon the Lyapunov method, and the global finite-time Lyapunov stability rather than the global finite-time convergence is established for the resulting closed-loop system by using the modified adding a power integrator technique. On this basis, a quasi-continuous 2-sliding mode algorithm is further developed, and the chattering problem can be considerably reduced. Simulation results show that the control strategies proposed in this paper are effective.