Design of decentralized stabilizing variable structure controller for perturbed large-scale systems with delays in state

A design approach of decentralized stabilizing variable structure control for perturbed large-scale systems with delays in state variables is proposed in this paper. The control design includes both the decentralized variable structure control law and an integral type of switching hyperplane. First, the decentralized control law is derived in such a way that the global reaching condition is satisfied, so that the sliding mode occurs in each subsystem. Moreover, a switching hyperplane is designed to force the initial states of the overall system to lie on the sliding hyperplane when time is at zero, and the stability degree of the overall system in sliding mode is achieved by choosing the elements of the hyperplane matrix. The proposed design approach does not need the solution of the Lyapunov equation or Riccati equation. The robust performance in sliding mode is discussed in detail. Finally, a numerical example is given to demonstrate the results