Multi-input sliding mode control of nonlinear uncertain affine systems

In this paper the multi-input sliding mode methodology for uncertain nonlinear system affine in the control is generalized to the case in which the matrix pre-multiplying the control in the state equation is uncertain, non constant and state-dependent. This property is inherited by the matrix multiplying the control in the sliding output dynamics, which is the nonlinear version of the well known High Frequency Gain Matrix. The considered problem appears to be at the same time of practical interest and not sufficiently emphasized in the literature. The proposed solution is applicable to matrices, the eigenvalues of which, for any time and state, are positive and is based on the combination of the unit vector discontinuous control strategy with the recently introduced integral sliding mode method.