Robust adaptive SMC for uncertain singular delayed systems via observer

This article is focused on state-estimation-based adaptive control design for uncertain singular systems subject to state delay and uncertain nonlinearity by employing sliding mode technique. Firstly, the unmeasured state variables are generated by a particular observer without any inputs, and a new switching surface function of linear type is presented. In view of linear matrix inequality technique, the motion of the closed-loop system on the sliding surface is analysed, and new admissibility criteria are deduced. Then a switching controller with adaptive rules is synthesised to ensure the established sliding surface can be attained in finite moment. Finally, an illustrative example is proposed to demonstrate the feasibility of the theoretical method.