Second-Order Sliding Mode Controller Design Subject to an Upper-Triangular Structure

The second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics subject to an upper-triangular structure has been discussed in this paper. The proposed SOSM controller design involves two steps. First, a Lyapunov-based SOSM controller is developed by using the adding a power integrator technique to locally finite-time stabilize the sliding variables. Second, by combining the local SOSM controller with a saturation function, a novel SOSM controller with a saturation level is constructed. The feature of the new SOSM controller lies in that the saturation level can be tuned not only to guarantee the global convergence but also to improve the dynamic performance. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop sliding mode dynamics. The proposed method is eventually demonstrated by simulation results.

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