Design of robust sliding-mode output-feedback control with suboptimal guaranteed cost

The design approach of robust sliding-mode output-feedback (SMOF) controller in static nature is proposed for a class of uncertain systems with mismatched uncertainty in the state matrix. The main contribution of the approach is in that the quadratic performance can be optimised with guaranteed cost. At first, a new existence condition of linear sliding surface with guaranteed cost is derived, which only involves the original system parameters. Secondly, based on the existence condition, an iterative linear matrix inequality approach is proposed to optimise the quadratic performance on the sliding surface. At last, by using linear matrix inequalities approach, a design framework for synthesising the SMOF controller is presented, as a consequence, finite time convergence to the sliding mode can be guaranteed and, the quadratic performance can be optimised under input constraints. The superiority of the proposed method is verified by numeric examples.