Decentralized variable structure control of interconnected large scale system with uncertainties

A variable structure asymptotically stabilizing control law is proposed for the interconnected large scale systems with uncertainties. The switch surface is designed by making use of the left eigenvectors, and a soft boundary layer is built near the ideal switch surface by using an auxiliary function to make the control law continuous. The Lyapunov stability theory and the diagonal dominant property are used to prove the global asymptotic stability of the interconnected large scale system with uncertainties and with the variable structure control applied. The variable structure control makes the system quickly entering into the sliding mode and eliminates chattering near the switch surface. An illustrative example is given to verify the effectiveness of the method.