On the multi-input second-order sliding mode control of nonlinear uncertain systems

This note addresses the multi-input second-order sliding mode control design for a class of nonlinear multivariable uncertain dynamics. Among the most important peculiarities of the considered control problem, the considered sliding vector variable has a uniform vector relative degree [2,2, â∥,2] with respect to the vector control variable, and only the sign of the sliding vector and of its derivative are available for feedback. Additionally, the symmetric part of the state-dependent control matrix is supposed to be positive definite. Under some further mild restrictions on the uncertain system's dynamics, a control algorithm that realizes a multi-input version of the 'twisting' second-order sliding mode control algorithm is suggested. Simple controller tuning conditions are derived by means of a constructive Lyapunov analysis, which demonstrates that the suggested control algorithm guarantees the semiglobal asymptotic convergence to the sliding manifold. Simulation results, which confirm the good performance of the proposed scheme and investigate the actual accuracy obtained under the discrete-time implementation effects, are given.