Design of adaptively integral sliding mode controllers for delayed linear systems with mismatched uncertainties: A delay partitioning approach

In this paper, the problem of sliding mode control (SMC) for mismatched uncertain system is investigated. Some delay dependent robust asymptotical stability conditions are provided. Firstly, we give a lemma. By this lemma, a delay-dependent sufficient condition is presented by means of linear matrix inequalities (LMIs) which makes sliding mode dynamics asymptotically stable. Secondly, an adaptive integral sliding mode control is given to guarantee the sliding mode reaching condition in finite time with the upper bound of external disturbance unknown. In order to reduce the conservativeness of the obtained stability condition, we present a new sufficient condition by means of delay-time partitioning approach. A numerical example is provided to demonstrate the effectiveness of the proposed method.