High order sliding-mode control for uncertain nonlinear systems with relative degree three

A novel high order sliding-mode control is proposed based on finite state machine by combination of relay algorithm and an improved second order algorithm to solve uncertain nonlinear system stabilization with relative degree three in finite time. This approach drives finite state machines to switch according to sliding variable and first order derivative of it, forces sliding variable, first order derivative and second order derivative of it to zero, without the knowledge of second order derivative of sliding variable, and stabilizes the system in finite time.

► A novel high order sliding-mode control for nonlinear system stabilization with relative degree three is given.
► The proposed algorithm needs not the estimate for the second order derivative of sliding variable.
► Several numerical simulations illustrate the theoretical analysis.
► Some simulations also illustrate the performance of control systems with two different switch frequencies.