Variable structure control of polytopic systems with time-delay

In this paper, the problem of designing a variable structure control is investigated for uncertain polytopic systems with time-delay. Firstly, by employing linear matrix inequality (LMI) method, a sufficient condition is derived for the existence of linear sliding model. Secondly, the variable structure control law is designed, which not only guarantees the system to reach the sliding model in finite time, but also assures it to be robust quadratic stable on the sliding surface. Finally, a numerical example illustrates the feasibility and effectiveness of the proposed method.