Design of static output feedback sliding mode control for uncertain linear systems

This paper considers the problem of designing a sliding mode controller via static output feedback for a class of uncertain systems with mismatched uncertainty in the state matrix. First, we derive a new existence condition of linear sliding surface in terms of strict linear matrix inequalities (LMIs) and propose an adaptive reaching control law such that the motion of the closed-loop system satisfies the reaching condition. Second, we further consider the delay-type switching function, and a new robust stability condition is given in terms of LMIs for the reduced-order sliding mode dynamics. Then, a synthesis procedure is established to design the sliding surface parameters. Finally, three examples, including an aircraft model, are utilized to illustrate the design procedures proposed in this paper.